论文信息 - Nonlinear Stochastic Difference Equations Driven by Martingales

Nonlinear Stochastic Difference Equations Driven by Martingales

Abstract We provide in this paper a systematic development of nonlinear stochastic difference equations driven by martingales (that depend on a spatial parameter); three such equations are considered. We begin with the existence and uniqueness of solutions and continue with the study of stochastic properties, such as the martingale and Markov properties, along with ϕ irreducibility and recurrence. We discuss in the final section the discrete-time flow and asymptotic flow properties of the solution process.

Bo Zhang | Jingxiao Zhang | D. Kannan

[1] D. Williams. STOCHASTIC DIFFERENTIAL EQUATIONS: THEORY AND APPLICATIONS , 1976 .

[2] J. Doob. Classical potential theory and its probabilistic counterpart , 1984 .

[3] Bo Zhang. A numerical analysis of stochastic neural networks , 2000, Neural Parallel Sci. Comput..

[4] DISCRETE-TIME MARTINGALES WITH SPATIAL PARAMETERS , 2002 .

[5] 国田寛. Stochastic flows and stochastic differential equations , 1990 .

[6] E. Helfand. Numerical integration of stochastic differential equations , 1979, The Bell System Technical Journal.

[7] Diffusion approximations of some stochastic difference equations revisited , 1988 .

[8] A DISCRETE-TIME ITÔ'S FORMULA , 2002 .

[9] Richard L. Tweedie,et al. Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[10] Mtw,et al. Stochastic flows and stochastic differential equations , 1990 .