Abstract
This paper studies the existence and uniqueness of the following kind of backward stochastic nonlinear Volterra integral equation under global Lipschitz condition, where {W t ;t∈[0,T]} is a standard k-dimensional Wiener process defined on a probability space {Ω,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∈[0,T],s∈[t,T]} with values in R d and R d×k respectively, which solves the above equation. This paper also generalize our results to the following equation: under rather restrictive assumptions on g. *This research was supported by the National Natural Science Foundation of China, program no. 79790130.
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