Adapted solution of a backward stochastic nonlinear Volterra integral equation

作者：Lin, JZ

来源：Stochastic Analysis and Applications, 2002, 20(1): 165-183.

DOI：10.1081/SAP-120002426

• backward stochastic differential equation
• backward stochastic nonlinear
• Volterra integral equation
• adapted process

This paper studies the existence and uniqueness of the following kind of backward stochastic nonlinear Volterra integral equation
x(t) integral(t)(T) f(t,s,X(s), Z(t,s))ds integral(t)(T) [g(t,s,X(s)) Z(t, s)] dW(s) =X
under global Lipschitz condition, where {W-t; t is an element of [0,T]} is a standard k-dimensional Wiener process defined on a probability space {Omega,F,F-t,P} and X is {F-T}measurable d-dimensional random vector. The problem is to look for an adapted pair of processes {X(t), Z(t, s); t is an element of [0,T], s is an element of [t, T]} with values in R-d and R-d x k respectively, which solves the above equation. This paper also generalize our results to the following equation:
X(t) integral(t)(T) f(t,s,X(s), Z(t,s))ds integral(t)(T) g(t,s,X(s), Z(t,s))dW(s) = X
under rather restrictive assumptions on g.

• 出版日期2002-1
• 单位上海交通大学