两参数鞅型非线性积分微分随机方程解的存在性轨道唯一性和收敛性

ON EXISTENCE, PATHWISE UNIQUENESS AND CONVERGENCEOF SOLUTIONS FOR THE NONLINEAR INTEGRODIFFERE NTIAL SDE WITH RESPECT TO THE MARTINGALE IN THE PLANE

摘要: 设M、A、C分别为R₊²=0,∞)×0,∞)上的两参数连续平方可积鞅和连续适应增过程.本文证明了随机方程（Ⅰ）\left\\beginarraylX_z=x_0+\int_R_f f\left(\xi, X_t, \int_R_t \alpha\left(\xi, \eta, X_\eta\right) d M_\eta, \int_R_t \beta\left(\xi, \eta, X_n\right) d A_n\right) d C_t, z \in R_+^2 \\ X_z=x_0,\endarray\right.解的存在性,轨道唯一性和收敛性成立.

Abstract: This paper is concerned with exitence, pathwise uniqueness and covergence of the solutions for the stochastic nonliear integrodifferential equations of form,\left\\beginarraylX_z=x_0+\int_R_f f\left(\xi, X_t, \int_R_t \alpha\left(\xi, \eta, X_\eta\right) d M_\eta, \int_R_t \beta\left(\xi, \eta, X_n\right) d A_n\right) d C_t, z \in R_+^2 \\ X_z=x_0,\endarray\right.,in the plane under suitabale conditions on the function involved in （1）, where M, A, C are the 2-parameter continuous square integrable martingale and continuous adapted increasing processes on R₊²=0, ∞)×0, ∞), respectively.