Strong Local Non-Determinism of Sub-Fractional Brownian Motion

Let be a subfractional Brownian motion in . We prove that is strongly locally nondeterministic.

Mixed Sub-fractional Brownian Motion and Drift Estimation of Related Ornstein-Uhlenbeck Process

In this paper,wewill first give the numerical simulation of the sub-fractional Brownian motion through the relation of fractional Brownian motion instead of its representation of random walk.In order to verify the rationality of this simulation,we propose a practical estimator associated with the LSE of the drift parameter of mixed sub-fractional Ornstein-Uhlenbeck process,and illustrate the asymptotical properties according to our method of simulation when the Hurst parameter H>1/2.

The generalized Bouleau-Yor identity for a sub-fractional Brownian motion

Let SH be a sub-fractional Brownian motion with index 0 〈 H 〈 1/2. In this paper we study the existence of the generalized quadratic eovariation [f（SH）, SH]（W） defined by[f（SH）,SH]t（W）=lim ε↓0 1/ ε2H ∫t 0 {f（SH s＋ε）-f（SH s＋ε）-f（SH s）}（SH s＋ε -SH s）ds2H, provided the limit exists in probability, where x → f（x） is a measurable function. We construct a Banach space X of measurable functions such that the generalized quadratic covariation exists in L2 provided f ∈ X. Moreover, the generalized Bouleau-Yor identity takes the form -∫R f（x） H（dx,t）=（2-2 2H-1）[f（SH ）,SH]t（w） for all f ∈ where H （X, t） is the weighted local time of SH. This allows us to write the generalized ItS＇s formula for absolutely continuous functions with derivative belonging to .

Influence of Brownian Motion, Thermophoresis and Magnetic Effects on a Fluid Containing Nanoparticles Flowing over a Stretchable Cylinder

The influence of Brownian motion and thermophoresis on a fluid containing nanoparticles flowing over a stretchable cylinder is examined.The classical Navier-Stokes equations are considered in a porous frame.In addition,the Lorentz force is taken into account.The controlling coupled nonlinear partial differential equations are transformed into a system of first order ordinary differential equations by means of a similarity transformation.The resulting system of equations is solved by employing a shooting approach properly implemented in MATLAB.The evolution of the boundary layer and the growing velocity is shown graphically together with the related profiles of concentration and temperature.The magnetic field has a different influence(in terms of trends)on velocity and concentration.

Nonparametric Estimation of the Trend Function for Stochastic Processes Driven by Fractional Brownian Motion of the Second Kind

The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.

Computational Investigation of Brownian Motion and Thermophoresis Effect on Blood-Based Casson Nanofluid on a Non-linearly Stretching Sheet with Ohmic and Viscous Dissipation Effects

Motivated by the widespread applications of nanofluids,a nanofluid model is proposed which focuses on uniform magnetohydrodynamic(MHD)boundary layer flow over a non-linear stretching sheet,incorporating the Casson model for blood-based nanofluid while accounting for viscous and Ohmic dissipation effects under the cases of Constant Surface Temperature(CST)and Prescribed Surface Temperature(PST).The study employs a twophase model for the nanofluid,coupled with thermophoresis and Brownian motion,to analyze the effects of key fluid parameters such as thermophoresis,Brownian motion,slip velocity,Schmidt number,Eckert number,magnetic parameter,and non-linear stretching parameter on the velocity,concentration,and temperature profiles of the nanofluid.The proposed model is novel as it simultaneously considers the impact of thermophoresis and Brownian motion,along with Ohmic and viscous dissipation effects,in both CST and PST scenarios for blood-based Casson nanofluid.The numerical technique built into MATLAB’s bvp4c module is utilized to solve the governing system of coupled differential equations,revealing that the concentration of nanoparticles decreases with increasing thermophoresis and Brownian motion parameters while the temperature of the nanofluid increases.Additionally,a higher Eckert number is found to reduce the nanofluid temperature.A comparative analysis between CST and PST scenarios is also undertaken,which highlights the significant influence of these factors on the fluid’s characteristics.The findings have potential applications in biomedical processes to enhance fluid velocity and heat transfer rates,ultimately improving patient outcomes.

On a Compound Poisson Risk Model Perturbed by Brownian Motion with Variable Premium and Tail Dependence between Claims Amounts and Inter-Claim Time

This paper considers the compound Poisson risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. It is assumed that the insurance company’s portfolio is governed by two classes of policyholders. On the one hand, the first class where the amount of claims is high, and on the other hand, the second class where the amount of claims is low, this difference in claim amounts has significant implications for the insurance company’s pricing and risk management strategies. When policyholders are in the first class, they pay an insurance premium of a constant amount c1 and when they are in the second class, the premium paid is a constant amount c2 such that c1 > c2. The nature of claims (low or high) is measured via random thresholds . The study in this work will focus on the determination of the integro-differential equations satisfied by Gerber-Shiu functions and their Laplace transforms in the risk model perturbed by Brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. .

HARNACK TYPE INEQUALITIES FOR SDES DRIVEN BY FRACTIONAL BROWNIAN MOTION WITH MARKOVIAN SWITCHING

In this paper, by constructing a coupling equation, we establish the Harnack type inequalities for stochastic differential equations driven by fractional Brownian motion with Markovian switching. The Hurst parameter H is supposed to be in(1/2, 1). As a direct application, the strong Feller property is presented.

On the sub-mixed fractional Brownian motion

Let {S t H, t ≥ 0） be a linear combination of a Brownian motion and an independent sub-fractional Brownian motion with Hurst index 0 〈 H 〈 1. Its main properties are studied. They suggest that SH lies between the sub-fractional Brownian motion and the mixed fractional Brownian motion. We also determine the values of H for which SH is not a semi-martingale.

从x出发的漂移Brownian Motion的极值分布

该文研究了从x出发的正漂移Brownian Motion的极值问题,给出了关于这种随机过程的两种极大值的定义,并主要利用Brownian Motion的一些重要性质,比如正交不变性、时空齐次性及在有限停时上的强Markov性等,获得了两种极大值的分布函数的精确表达式.

REMARKS ON SUB-FRACTIONAL BESSEL PROCESSES

Let S = {（St1,···,Std ）}t≥0 denote a d-dimensional sub-fractional Brownian motion with index H ≥ 1/2. In this paper we study some properties of the process X of the formwhere Rt = （（St1）2＋···＋（Std）2）~1/2 is the sub-fractional Bessel process.

Polar Functions for Fractional Brownian Motion

Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the class of polar functions are studied. Our theorem 1 improves the previous results of Graversen and Legall. Theorem2 solves a problem of Legall (1987) on Brownian motion.

Thermophoresis and Brownian motion effects on boundary layer flow of nanofluid in presence of thermal stratification due to solar energy

The problem of laminar fluid flow, which results from the stretching of a vertical surface with variable stream conditions in a nanofluid due to solar energy, is in- vestigated numerically. The model used for the nanofluid incorporates the effects of the Brownian motion and thermophoresis in the presence of thermal stratification. The sym- metry groups admitted by the corresponding boundary value problem are obtained by using a special form of Lie group transformations, namely, the scaling group of transfor- mations. An exact solution is obtained for the translation symmetrys, and the numerical solutions are obtained for the scaling symmetry. This solution depends on the Lewis number, the Brownian motion parameter, the thermal stratification parameter, and the thermophoretic parameter. The conclusion is drawn that the flow field, the temperature, and the nanoparticle volume fraction profiles are significantly influenced by these param- eters. Nanofluids have been shown to increase the thermal conductivity and convective heat transfer performance of base liquids. Nanoparticles in the base fluids also offer the potential in improving the radiative properties of the liquids, leading to an increase in the efficiency of direct absorption solar collectors.

On p-variation of bifractional Brownian motion

In this paper we study p-variation of bifractional Brownian motion. As an applica-tion, we introduce a class of estimators of the parameters of a bifractional Brownian motion andprove that both of them are strongly consistent; as another application, we investigate fractalnature related to the box dimension of the graph of bifractional Brownian motion.

EXACT MAXIMUM LIKELIHOOD ESTIMATOR FOR DRIFT FRACTIONAL BROWNIAN MOTION AT DISCRETE OBSERVATION

This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.

POWER VARIATION OF SUBFRACTIONAL BROWNIAN MOTION AND APPLICATION

In this paper, we consider the power variation of subfractional Brownian mo- tion. As an application, we introduce a class of estimators for the index of a subfractional Brownian motion and show that they are strongly consistent.

LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION

In this article, we study a least squares estimator （LSE） of θ for the Ornstein- Uhlenbeck process X0=0,dXt=θXtdt＋dBt^ab, t ≥ 0 driven by weighted fractional Brownian motion B^a,b with parameters a, b. We obtain the consistency and the asymptotic distribution of the LSE based on the observation {Xs, s∈[0,t]} as t tends to infinity.

Brownian Motion and the Temperament of Living Cells

The migration of living cells usually obeys the laws of Brownian motion.While the latter is due to the thermal motion of the surrounding matter,the locomotion of cells is generally associated with their vitality.We study what drives cell migration and how to model memory effects in the Brownian motion of cells.The concept of temperament is introduced as an effective biophysical parameter driving the motion of living biological entities in analogy with the physical parameter of temperature,which dictates the movement of lifeless physical objects.The locomemory of cells is also studied via the generalized Langevin equation.We explore the possibility of describing cell locomemory via the Brownian self-similarity concept.An heuristic expression for the diffusion coefficient of cells on structured surfaces is derived.

AN ENLARGEMENT OF FILTRATION FOR BROWNIAN MOTION

Let Bt be an Ft Brownian motion and Gt be an enlargement of filtration of Ft from some Gaussian random variables. We obtain equations for ht such that Bt ht is a Gt-Brownian motion.

SOME CENTRAL LIMIT THEOREMS FOR SUPER BROWNIAN MOTION

The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limiting field is the same aa that obtained by Dawson (1977). In the recurrent case it is a spatially uniform field. The author also give a central limit theorem for the weighted occupation time of the super Brownian motion with underlying dimension number d less than or equal to 3, completing the results of Iscoe (1986).