Improvements of corner frequency and scaling factor for stochastic finite-fault modeling

In this paper, three existing source spectral models for stochastic finite-fault modeling of ground motion were reviewed. These three models were used to calculate the far-field received energy at a site from a vertical fault and the mean spectral ratio over 15 stations of the Northridge earthquake, and then compared. From the comparison, a necessary measure was observed to maintain the far-field received energy independent of subfault size and avoid overestimation of the long- period spectra/level. Two improvements were made to one of the three models （i.e., the model based on dynamic comer frequency） as follows： （i） a new method to compute the subfault comer frequency was proposed, where the subfault comer frequency is determined based on a basic value calculated from the total seismic moment of the entire fault and an increment depending on the seismic moment assigned to the subfault; and （ii） the difference of the radiation energy from each suhfault was considered into the scaling factor. The improved model was also compared with the unimproved model through the far-field received energy and the mean spectral ratio. The comparison proves that the improved model allows the received energy to be more independent of subfault size than the unimproved model, and decreases the overestimation degree of the long-period spectral amplitude.

Seismic ground motion relationships in southern China based on stochastic finite-fault model

The characteristics of seismic ground motions in southern China are difficult to determine statistically due to a lack of strong ground motion data.In this study,a stochastic finite-fault ground motion model was adopted to simulate the seismic ground motions at bedrock for southern China,based on parameters derived from small and medium earthquakes that have occurred in the region.From these,the response spectra was estimated.A set of ground motion attenuation relationships was then developed based on simulated peak ground motions and response spectral parameters through regression,which would be applicable for use in engineering practice.Through comparisons,it was demonstrated that the proposed ground motion relationships are generally consistent with those obtained from other reported ground motion attenuation models for southern China.

Analytical and NumericalMethods to Study the MFPT and SR of a Stochastic Tumor-Immune Model

The Mean First-Passage Time (MFPT) and Stochastic Resonance (SR) of a stochastic tumor-immune model withnoise perturbation are discussed in this paper. Firstly, considering environmental perturbation, Gaussian whitenoise and Gaussian colored noise are introduced into a tumor growth model under immune surveillance. Asfollows, the long-time evolution of the tumor characterized by the Stationary Probability Density (SPD) and MFPTis obtained in theory on the basis of the Approximated Fokker-Planck Equation (AFPE). Herein the recurrenceof the tumor from the extinction state to the tumor-present state is more concerned in this paper. A moreefficient algorithmof Back-Propagation Neural Network (BPNN) is utilized in order to testify the correction of thetheoretical SPDandMFPT.With the existence of aweak signal, the functional relationship between Signal-to-NoiseRatio (SNR), noise intensities and correlation time is also studied. Numerical results show that both multiplicativeGaussian colored noise and additive Gaussian white noise can promote the extinction of the tumors, and themultiplicative Gaussian colored noise can lead to the resonance-like peak on MFPT curves, while the increasingintensity of the additiveGaussian white noise results in theminimum of MFPT. In addition, the correlation timesare negatively correlated with MFPT. As for the SNR, we find the intensities of both the Gaussian white noise andthe Gaussian colored noise, as well as their correlation intensity can induce SR. Especially, SNR is monotonouslyincreased in the case ofGaussian white noisewith the change of the correlation time.At last, the optimal parametersin BPNN structure are analyzed for MFPT from three aspects: the penalty factors, the number of neural networklayers and the number of nodes in each layer.

A modified stochastic finite-fault method for estimating strong ground motion:Validation and application

We developed a modified stochastic finite-fault method for estimating strong ground motions.An adjustment to the dynamic corner frequency was introduced,which accounted for the effect of the location of the subfault relative to the hypocenter and rupture propagation direction,to account for the influence of the rupture propagation direction on the subfault dynamic corner frequency.By comparing the peak ground acceleration(PGA),pseudo-absolute response spectra acceleration(PSA,damping ratio of 5%),and duration,the results of the modified and existing methods were compared,demonstrating that our proposed adjustment to the dynamic corner frequency can accurately reflect the rupture directivity effect.We applied our modified method to simulate near-field strong motions within 150 km of the 2008 MW7.9 Wenchuan earthquake rupture.Our modified method performed well over a broad period range,particularly at 0.04-4 s.The total deviations of the stochastic finite-fault method(EXSIM)and the modified EXSIM were 0.1676 and 0.1494,respectively.The modified method can effectively account for the influence of the rupture propagation direction and provide more realistic ground motion estimations for earthquake disaster mitigation.

Stochastic seismic inversion and Bayesian facies classification applied to porosity modeling and igneous rock identification

We apply stochastic seismic inversion and Bayesian facies classification for porosity modeling and igneous rock identification in the presalt interval of the Santos Basin. This integration of seismic and well-derived information enhances reservoir characterization. Stochastic inversion and Bayesian classification are powerful tools because they permit addressing the uncertainties in the model. We used the ES-MDA algorithm to achieve the realizations equivalent to the percentiles P10, P50, and P90 of acoustic impedance, a novel method for acoustic inversion in presalt. The facies were divided into five: reservoir 1,reservoir 2, tight carbonates, clayey rocks, and igneous rocks. To deal with the overlaps in acoustic impedance values of facies, we included geological information using a priori probability, indicating that structural highs are reservoir-dominated. To illustrate our approach, we conducted porosity modeling using facies-related rock-physics models for rock-physics inversion in an area with a well drilled in a coquina bank and evaluated the thickness and extension of an igneous intrusion near the carbonate-salt interface. The modeled porosity and the classified seismic facies are in good agreement with the ones observed in the wells. Notably, the coquinas bank presents an improvement in the porosity towards the top. The a priori probability model was crucial for limiting the clayey rocks to the structural lows. In Well B, the hit rate of the igneous rock in the three scenarios is higher than 60%, showing an excellent thickness-prediction capability.

A modified stochastic model for LS+AR hybrid method and its application in polar motion short-term prediction

Short-term(up to 30 days)predictions of Earth Rotation Parameters(ERPs)such as Polar Motion(PM:PMX and PMY)play an essential role in real-time applications related to high-precision reference frame conversion.Currently,least squares(LS)+auto-regressive(AR)hybrid method is one of the main techniques of PM prediction.Besides,the weighted LS+AR hybrid method performs well for PM short-term prediction.However,the corresponding covariance information of LS fitting residuals deserves further exploration in the AR model.In this study,we have derived a modified stochastic model for the LS+AR hybrid method,namely the weighted LS+weighted AR hybrid method.By using the PM data products of IERS EOP 14 C04,the numerical results indicate that for PM short-term forecasting,the proposed weighted LS+weighted AR hybrid method shows an advantage over both the LS+AR hybrid method and the weighted LS+AR hybrid method.Compared to the mean absolute errors(MAEs)of PMX/PMY sho rt-term prediction of the LS+AR hybrid method and the weighted LS+AR hybrid method,the weighted LS+weighted AR hybrid method shows average improvements of 6.61%/12.08%and 0.24%/11.65%,respectively.Besides,for the slopes of the linear regression lines fitted to the errors of each method,the growth of the prediction error of the proposed method is slower than that of the other two methods.

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.

Stochastic Maximum Principle for Optimal Advertising Models with Delay and Non-Convex Control Spaces

In this paper we study optimal advertising problems that model the introduction of a new product into the market in the presence of carryover effects of the advertisement and with memory effects in the level of goodwill. In particular, we let the dynamics of the product goodwill to depend on the past, and also on past advertising efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for a class of problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of controls U can be chosen to be non-convex but now the space of controls U can be chosen to be non-convex. The maximum principle is thus formulated using a first-order adjoint Backward Stochastic Differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.

Stochastic Analysis and Modeling of Velocity Observations in Turbulent Flows

Highly turbulent water flows,often encountered near human constructions like bridge piers,spillways,and weirs,display intricate dynamics characterized by the formation of eddies and vortices.These formations,varying in sizes and lifespans,significantly influence the distribution of fluid velocities within the flow.Subsequently,the rapid velocity fluctuations in highly turbulent flows lead to elevated shear and normal stress levels.For this reason,to meticulously study these dynamics,more often than not,physical modeling is employed for studying the impact of turbulent flows on the stability and longevity of nearby structures.Despite the effectiveness of physical modeling,various monitoring challenges arise,including flow disruption,the necessity for concurrent gauging at multiple locations,and the duration of measurements.Addressing these challenges,image velocimetry emerges as an ideal method in fluid mechanics,particularly for studying turbulent flows.To account for measurement duration,a probabilistic approach utilizing a probability density function(PDF)is suggested to mitigate uncertainty in estimated average and maximum values.However,it becomes evident that deriving the PDF is not straightforward for all turbulence-induced stresses.In response,this study proposes a novel approach by combining image velocimetry with a stochastic model to provide a generic yet accurate description of flow dynamics in such applications.This integration enables an approach based on the probability of failure,facilitating a more comprehensive analysis of turbulent flows.Such an approach is essential for estimating both short-and long-term stresses on hydraulic constructions under assessment.

Stochastic Bifurcation of an SIS Epidemic Model with Treatment and Immigration

In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochastic system by computing the Lyapunov exponent of the linearized system. Further, the global stability of the stochastic model is analyzed based on the singular boundary theory. Moreover, we prove that the model undergoes a Hopf bifurcation and a pitchfork bifurcation. Finally, several numerical examples are provided to illustrate the theoretical results. .

Asymptotic Analysis of a Stochastic Model of Mosquito-Borne Disease with the Use of Insecticides and Bet Nets

Ross’ epidemic model describing the transmission of malaria uses two classes of infection, one for humans and one for mosquitoes. This paper presents a stochastic extension of a deterministic vector-borne epidemic model based only on the class of human infectious. The consistency of the model is established by proving that the stochastic delay differential equation describing the model has a unique positive global solution. The extinction of the disease is studied through the analysis of the stability of the disease-free equilibrium state and the persistence of the model. Finally, we introduce some numerical simulations to illustrate the obtained results.

Research and application of composite stochastic resonance in enhancement detection

Aiming at the problem that the intermediate potential part of the traditional bistable stochastic resonance model cannot be adjusted independently, a new composite stochastic resonance(NCSR) model is proposed by combining the Woods–Saxon(WS) model and the improved piecewise bistable model. The model retains the characteristics of the independent parameters of WS model and the improved piecewise model has no output saturation, all the parameters in the new model have no coupling characteristics. Under α stable noise environment, the new model is used to detect periodic signal and aperiodic signal, the detection results indicate that the new model has higher noise utilization and better detection effect.Finally, the new model is applied to image denoising, the results showed that under the same conditions, the output peak signal-to-noise ratio(PSNR) and the correlation number of NCSR method is higher than that of other commonly used linear denoising methods and improved piecewise SR methods, the effectiveness of the new model is verified.

A stochastic two-dimensional intelligent driver car-following model with vehicular dynamics

The law of vehicle movement has long been studied under the umbrella of microscopic traffic flow models,especially the car-following(CF)models.These models of the movement of vehicles serve as the backbone of traffic flow analysis,simulation,autonomous vehicle development,etc.Two-dimensional(2D)vehicular movement is basically stochastic and is the result of interactions between a driver's behavior and a vehicle's characteristics.Current microscopic models either neglect 2D noise,or overlook vehicle dynamics.The modeling capabilities,thus,are limited,so that stochastic lateral movement cannot be reproduced.The present research extends an intelligent driver model(IDM)by explicitly considering both vehicle dynamics and 2D noises to formulate a stochastic 2D IDM model,with vehicle dynamics based on the stochastic differential equation(SDE)theory.Control inputs from the vehicle include the steer rate and longitudinal acceleration,both of which are developed based on an idea from a traditional intelligent driver model.The stochastic stability condition is analyzed on the basis of Lyapunov theory.Numerical analysis is used to assess the two cases:(i)when a vehicle accelerates from a standstill and(ii)when a platoon of vehicles follow a leader with a stop-and-go speed profile,the formation of congestion and subsequent dispersion are simulated.The results show that the model can reproduce the stochastic 2D trajectories of the vehicle and the marginal distribution of lateral movement.The proposed model can be used in both a simulation platform and a behavioral analysis of a human driver in traffic flow.

Exit problem of stochastic SIR model with limited medical resource

Nonlinearity and randomness are both the essential attributes for the real world,and the case is the same for the models of infectious diseases,for which the deterministic models can not give a complete picture of the evolution.However,although there has been a lot of work on stochastic epidemic models,most of them focus mainly on qualitative properties,which makes us somewhat ignore the original meaning of the parameter value.In this paper we extend the classic susceptible-infectious-removed(SIR)epidemic model by adding a white noise excitation and then we utilize the large deviation theory to quantitatively study the long-term coexistence exit problem with epidemic.Finally,in order to extend the meaning of parameters in the corresponding deterministic system,we tentatively introduce two new thresholds which then prove rational.

Stochastic Models to Mitigate Sparse Sensor Attacks in Continuous-Time Non-Linear Cyber-Physical Systems

Cyber-Physical Systems are very vulnerable to sparse sensor attacks.But current protection mechanisms employ linear and deterministic models which cannot detect attacks precisely.Therefore,in this paper,we propose a new non-linear generalized model to describe Cyber-Physical Systems.This model includes unknown multivariable discrete and continuous-time functions and different multiplicative noises to represent the evolution of physical processes and randomeffects in the physical and computationalworlds.Besides,the digitalization stage in hardware devices is represented too.Attackers and most critical sparse sensor attacks are described through a stochastic process.The reconstruction and protectionmechanisms are based on aweighted stochasticmodel.Error probability in data samples is estimated through different indicators commonly employed in non-linear dynamics(such as the Fourier transform,first-return maps,or the probability density function).A decision algorithm calculates the final reconstructed value considering the previous error probability.An experimental validation based on simulation tools and real deployments is also carried out.Both,the new technology performance and scalability are studied.Results prove that the proposed solution protects Cyber-Physical Systems against up to 92%of attacks and perturbations,with a computational delay below 2.5 s.The proposed model shows a linear complexity,as recursive or iterative structures are not employed,just algebraic and probabilistic functions.In conclusion,the new model and reconstructionmechanism can protect successfully Cyber-Physical Systems against sparse sensor attacks,even in dense or pervasive deployments and scenarios.

The Stochastic Asymptotic Stability Analysis in Two Species Lotka-Volterra Model

The asymptotic stability of two species stochastic Lotka-Volterra model is explored in this paper. Firstly, the Lotka-Volterra model with random parameter is built and reduced into the equivalent deterministic system by orthogonal polynomial approximation. Then, the linear stability theory and Routh-Hurwitz criterion for nonlinear deterministic systems are applied to the equivalent one. At last, at the aid of Lyapunov second method, we obtain that as the random intensity or statistical parameter of random variable is changed, the stability about stochastic Lotka-Volterra model is different from the deterministic system.

Deterministic and Stochastic Analysis of a New Rumor Propagation Model with Nonlinear Propagation Rate in Social Network

This paper presents a study on a new rumor propagation model with nonlinear propagation rate and secondary propagation rate. We divide the total population into three groups, the ignorant, the spreader and the aware. The nonlinear incidence rate describes the psychological impact of certain serious rumors on social groups when the number of individuals spreading rumors becomes larger. The main contributions of this work are the development of a new rumor propagation model and some results of deterministic and stochastic analysis of the rumor propagation model. The results show the influence of nonlinear propagation rate and stochastic fluctuation on the dynamic behavior of the rumor propagation model by using Lyapunov function method and stochastic related knowledge. Numerical examples and simulation results are given to illustrate the results obtained.

Optimal Quota-Share and Excess-of-Loss Reinsurance and Investment with Heston’s Stochastic Volatility Model

An optimal quota-share and excess-of-loss reinsurance and investment problem is studied for an insurer who is allowed to invest in a risk-free asset and a risky asset.Especially the price process of the risky asset is governed by Heston's stochastic volatility(SV)model.With the objective of maximizing the expected index utility of the terminal wealth of the insurance company,by using the classical tools of stochastic optimal control,the explicit expressions for optimal strategies and optimal value functions are derived.An interesting conclusion is found that it is better to buy one reinsurance than two under the assumption of this paper.Moreover,some numerical simulations and sensitivity analysis are provided.

Parameter estimation of the stochastic AMR model and its application to the study of several strong earthquakes

Based on the stochastic AMR model, this paper constructs man-made earthquake catalogues to investigate the property of parameter estimation of the model. Then the stochastic AMR model is applied to the study of several strong earthquakes in China and New Zealand. Akaikes AIC criterion is used to discriminate whether an accelerating mode of earthquake activity precedes those events or not. Finally, regional accelerating seismic activity and possible prediction approach for future strong earthquakes are discussed.

A CLASS OF STATIONARY MODELS OF SINGULAR STOCHASTIC CONTROL

A class of stationary models of singular stochastic control has been studied, in which the state is extended to solution of a class of S.D.E. from Wiener process. The existence of optimal control has been proved in all cases under some weaker conditions, and the structure of optimal control may be characterized.