带交互作用测度值分枝过程的绝对连续性

本文研究Meleard-Roelly（1992，1993）和Metivier（1987）构造的带交互作用的测度值分枝过程的状态性质．我们证明在自然假设下该过程关于Lebesgue测度是绝对连续的，其密度有连续修正且满足一个随机偏微分方程．     

Stochastic equations for two-type continuous-state branching processes with immigration

A two-dimensional stochastic integral equation system with jumps is studied. We first prove its unique weak solution is a two-type continuous-state branching process with immigration. Then the comparison property of the solution is established. These results imply the existence and uniqueness of the strong solution of the stochastic equation system.     

Stochastic equations for two-type continuous-state branching processes with immigration and competition

A class of two-type continuous-state branching processes with immigration and competition is constructed as the solution of a jump-type stochastic integral equation system. We first show that the stochastic equation system has a pathwise unique non-negative strong solution and then prove the comparison property of the solution.     

Nonlinear branching processes with immigration

The nonlinear branching process with immigration is constructed as the pathwise unique solution of a stochastic integral equation driven by Poisson random measures. Some criteria for the regularity, recurrence, ergodicity and strong ergodicity of the process are then established.     

Diffusion approximation of the two-type Galton-Watson process with mean matrix close to the identity

In this paper a diffusion approximation to the two-type Galton-Watson branching processes with mean matrix close to the identity is given in the form of Berstein stochastic differentials. An associated diffusion equation is found using an extension of the one-dimensional Bernstein technique. Expressions for the mean vector and covariance matrix of the diffusion approximation are derived.     

Branching of Solutions of the Abstract Kinetic Equation

In this paper, bifurcation of solutions of a special nonlinear operator equation used in mathematical physics is considered. In the case of an equation for which the Fréchet derivative of the associated operator is a locally perturbed Fredholm operator, sufficient conditions for branching of solutions are studied. The methodology of application of the formalism developed in the paper is demonstrated by the example of the Boltzmann equation.     

A limit theorem for branching one-dimensional periodic diffusion processes

We give almost sure convergence of appropriately normalized particle numbers in bounded domains of locally supercritical branching diffusion processes with one-dimensional periodic diffusions as their non-branching part processes. Some spectral properties of periodic diffusion operators including Hill's ones are also studied.     

Catalytic Discrete State Branching Models and Related Limit Theorems

Catalytic discrete state branching processes with immigration are defined as strong solutions of stochastic integral equations. We provide main limit theorems of those processes using different scalings. The class of limit processes of the theorems includes essentially all continuous state catalytic branching processes and spectrally positive regular affine processes.      

带移民的碰撞分枝过程的唯一性

本文提出了一种带移民的碰撞分枝过程,它由三部分组成:马氏分枝过程、碰撞分枝过程和状态独立的移民过程,给出了该过程正则性和唯一性判别准则。     

Immigration process in catalytic medium

The longtime behavior of the immigration process associated with a catalytic super-Brownian motion is studied. A large number law is proved in dimension d≤3 and a central limit theorem is proved for dimension d=3.     

催化介质中的超Ornstein-Uhlenbeck 过程

本文构造了催化介质中的Ornstein-Uhlenbeck过程,并在有限测试情形,证明了其persistence性质（d=1)。     

MEASURE-VALUED IMMIGRATION DIFFUSIONS AND GENERALIZED ORNSTEIN-UHLENBECK DIFFUSIONS

1.IntroductionLetAbeaboundedlinearoperatoronS(R')whichadmitsanon-positivedefiniteself-adjoillteXtensiononL'(R').AssumethatAgeneratesastronglycontinuoussellilgroupicofboundedlinearoperatorsonS(R').LetBbeaboundedlinearoperatoron).aamtheresultsof[l],wek...     

更新理论推理过程及其应用

更新过程和马尔可夫更新过程中均有相对应的更新方程,实际问题中有许多变量都满足更新方程.但是在运用更新方程时,对于一些感兴趣的变量很难直接套用更新方程,这就使更新方程在实际问题的应用有许多困难.针对这个问题,总结归纳了应用更新方程的更新理论推理过程,给出了具体的推理方法和步骤,并举例进行了说明.     

Optimal die shape for film casting

We consider an isothermal model for the film casting process. The aim of this study is to determine a shape of the die that leads to a uniform thickness of the film. Thanks to a decoupling of the equations for the thickness and the velocities of the film, we are able to solve the reverse thickness equation. This reverse equation describes the dependence of the shape of the die on the desired final thickness.     

鞅方法在一类破产问题中的应用

本文从鞅条件出发 ,推导出了总理赔过程分别为复合 Poisson过程与复合二项过程 ,利率强度波动为带跳的 Poisson过程情形下的调节方程 ,并由此得到了一些有趣的结果。     

Weak solutions to gamma-driven stochastic differential equations

We study a stochastic differential equation driven by a gamma process, for which we give results on the existence of weak solutions under conditions on the volatility function. To that end we provide results on the density process between the laws of solutions with different volatility functions.     

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.     

Group theoretic approach for solving the problem of diffusion of a drug through a thin membrane

The transformation group theoretic approach is applied to study the diffusion process of a drug through a skin-like membrane which tends to partially absorb the drug. Two cases are considered for the diffusion coefficient. The application of one parameter group reduces the number of independent variables by one, and consequently the partial differential equation governing the diffusion process with the boundary and initial conditions is transformed into an ordinary differential equation with the corresponding conditions. The obtained differential equation is solved numerically using the shooting method, and the results are illustrated graphically and in tables.     

Random creation and dispersion of mass

Consider evolution of density of a mass or a population, geographically situated in a compact region of space, assuming random creation-annihilation and migration, or dispersion of mass, so the evolution is a random measure. When the creation-annihilation and dispersion are diffusions the situation is described formally by a stochastic partial differential equation; ignoring dispersion make approximations to the initial density by atomic measures and if the corresponding discrete random measures converge “in law” to a unique random measure call it a solution. To account for dispersion Trotter's product formula is applied to semiflows corresponding to dispersion and creation-annihilation. Existence of solutions has been a conjecture for several years despite a claim in ([2], J. Multivariate Anal. 5, 1–52). We show that solutions exist and that non-deterministic solutions are “smeared” continuous-state branching diffusions.     

Diffusion-Approximations for Navier-Stokes Equation in Space-Time Gaussian Velocity Field

Abstract

By approximation methods, the existence of solutions for the Navier-Stokes equation with rapidly oscillating drift term for dimention 2 or 3 is proved. Also by the martingale method, stochastic Navier-Stokes equation is considered.