STOCHASTIC FLOWS OF MAPPINGS

In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.

State Descomposition of Superprocesses of Stochastic Flows

In this paper, we reconstruct the superprocesses of stochastic flows by martingale method, and prove that if and only if the infinitesimal particles never hit each other, then atomic part and diffuse part of this kind of superprocesses will be also superprocesses of stochastic flows. This result completely answers the open problem in .

The Construction of a Class of Measure-valued Processes of Stochastic Flows

In this article, we give a description of measure-valued processes with interactive stochastic flows. It is a unified construction for superprocesses with dependent spatial motion constructed by Dawson, LI, Wang and superprocesses of stochastic flows constructed by Ma and Xiang.

Asymptotic Flatness of Stochastic Flow on Manifolds

The aim of this article is to discuss a volume nullification property of thediffusion process determined by a stochastic differential equation on a manifold. LetX_t(x) be a diffusion process describing a flow of diffeomorphisms x→X_t (x) in a manifoldM, and K be a compact surface in M with positive finite Hausdorff measure. We presentconditions under which the area of X_t(K) goes to zero almost surely and in momentsas t→∞! in particular, the flow X_t(·) asymptotic nullifies the arc-lenth of orientedrectifiable arcs r: [0, 1]→M.

Large deviations for stochastic flows and their applications

Large deviations for stochastic flow solutions to SDEs containing a small parameter are studied. The obtained results are applied to establish a Cp, r-large deviation principle for stochastic flows and for solutions to anticipating SDEs. The recent results of Millet-Nualart-Sans and Yoshida are improved and refined.

Synchronization of Stochastic Two-Layer Geophysical Flows

In this paper, the two-layer quasigeostrophic flow model under stochastic wind forcing is considered. It is shown that when the layer depth or density differ- ence across the layers tends to zero, the dynamics on both layers synchronizes to an averaged geophysical flow model.

Maximum Probabilistic and Dynamic Traffic Load Effects onShort-to-Medium Span Bridges

The steadily growing traffic load has resulted in lots of bridge collapse events over the past decades, especiallyfor short-to-medium span bridges. This study investigated probabilistic and dynamic traffic load effects on shortto-medium span bridges using practical heavy traffic data in China. Mathematical formulations for traffic-bridgecoupled vibration and probabilistic extrapolation were derived. A framework for extrapolating probabilistic anddynamic traffic load effect was presented to conduct an efficient and accurate extrapolation. An equivalent dynamicwheel load model was demonstrated to be feasible for short-to-medium span bridges. Numerical studies of twotypes of simply-supported bridges were conducted based on site-specific traffic monitoring data. Numerical resultsshow that the simulated samples and fitting lines follow a curve line in the Gumbel distribution coordinate system. Itcan be assumed that dynamic traffic load effects follow Gaussian distribution and the extreme value follows Gumbeldistribution. The equivalent probabilistic amplification factor is smaller than the individual dynamic amplificationfactor, which might be due to the variability of individual samples. Eurocode 1 is the most conservative specificationon vehicle load models, followed by the BS5400 specification. The D60-2015 specification in China and ASSHTOspecification provide lower conservative traffic load models.

Stochastic simulation of fluid flow in porous media by the complex variable expression method

A stochastic simulation of fluid flow in porous media using a complex variable expression method （SFCM） is presented in this paper. Hydraulic conductivity is considered as a random variable and is then expressed in complex variable form, the real part of which is a deterministic value and the imaginary part is a variable value. The stochastic seepage flow is simulated with the SFCM and is compared with the results calculated with the Monte Carlo stochastic finite element method. In using the Monte Carlo method to simulate the stochastic seepage flow field, the hydraulic conductivity is assumed in three different probability distributions using random sampling method. The obtained seepage flow field is examined through skewness analysis, and the skewed distribution probability density function is given. The head mode value and the head comprehensive standard deviation are used to represent the statistics of calculation results obtained by the Monte Carlo method. The stochastic seepage flow field simulated by the SFCM is confirmed to be similar to that given by the Monte Carlo method from numerical aspects. The range of coefficient of variation of hydraulic conductivity in SFCM is larger than used previously in stochastic seepage flow field simulations, and the computation time is short. The results proved that the SFCM is a convenient calculating method for solving the complex problems.

Estimating Risk-aware Flexibility Areas for Electric Vehicle Charging Pools via AC Stochastic Optimal Power Flow

This paper introduces an AC stochastic optimal power flow(SOPF)for the flexibility management of electric vehicle(EV)charging pools in distribution networks under uncertainty.The AC SOPF considers discrete utility functions from charging pools as a compensation mechanism for eventual energy not served to their charging tasks.An application of the AC SOPF is described where a distribution system operator(DSO)requires flexibility to each charging pool in a day-ahead time frame,minimizing the cost for flexibility while guaranteeing technical limits.Flexibility areas are defined for each charging pool and calculated as a function of a risk parameter involving the uncertainty of the solution.Results show that all players can benefit from this approach,i.e.,the DSO obtains a riskaware solution,while charging pools/tasks perceive a reduction in the total energy payment due to flexibility services.

About One Discrete Mathematical Model of Perfect Fluid

In work, it is constructed a discrete mathematical model of motion of a perfect fluid. The fluid is represented as an ensemble of identical so-called liquid particles, which are in the form of extended geometrical objects: circles and spheres for two-dimensional and three-dimensional cases, respectively. The mechanism of interaction between the liquid particles on a binary level and on the level of the n-cluster is formulated. This mechanism has previously been found by the author as part of the mathematical modeling of turbulent fluid motion. In the turbulence model was derived and investigated the potential interaction of pairs of liquid particles, which contained a singularity of the branch point. Exactly, this is possible to build in this article discrete stochastic-deterministic model of an ideal fluid. The results of computational experiment to simulate various kinds of flows in two-dimensional and three-dimensional ensembles of liquid particles are presented. Modeling was carried out in the areas of quadratic or cubic form. On boundary of a region satisfies the condition of elastic reflection liquid particles. The flows with spontaneous separation of particles in a region, various kinds of eddy streams, with the quite unexpected statistical properties of an ensemble of particles characteristic for the Fermi-Pasta-Ulam effect were found. We build and study the flow in which the velocity of the particles is calibrated. It was possible using the appropriate flows of liquid particles of the ensemble to demonstrate the possibility to reproduce any prescribed image by manipulating the parameters of the interaction. Calculations of the flows were performed with using MATLAB software package according to the algorithms presented in this article.

SEMI-LINEAR SYSTEMS OF BACKWARD STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN R^n

This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs.The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.

Limit theorems for flows of branching processes

We construct two kinds of stochastic flows of discrete Galton-Watson branching processes. Some scaling limit theorems for the flows are proved, which lead to local and nonlocal branching superprocesses over the positive half line.

Perturbation analysis of stochastic hybrid systems and applications to resource contention games

We provide an overview of the recently developed general infinitesimal perturbation analysis(IPA)framework for stochastic hybrid systems(SHSs),and establish some conditions under which this framework can be used to obtain unbiased performance gradient estimates in a particularly simple and efficient manner.We also propose a general scheme for systematically deriving an abstraction of a discrete event system(DES)in the form of an SHS.Then,as an application of the general IPA framework,we study a class of stochastic non-cooperative games termed“resource contention games”modeled through stochastic flow models(SFMs),where two or more players(users)compete for the use of a sharable resource.Simulation results are provided for a simple version of such games to illustrate and contrast system-centric and user-centric optimization.

One Dimensional Stochastic Differential Equations with Distributional Drifts

In this paper we study the existence, pathwise uniqueness and homeomorphism flow of strong solutions to a class of one dimensional SDEs driven by infinitely many Brownian motions, and with Yamada- Watanabe diffusion coefficients and distributional drift coefficients.