The Equivalence between Uniqueness and Continuous Dependence of Solution for BDSDEs

Details The Equivalence between Uniqueness and Continuous Dependence of Solution for BDSDEs The Equivalence between Uniqueness and Continuous Dependence of Solution for BDSDEs

2010-05-14

arxiv.org/abs/1005.2477v1

Mathematics

Probability

11 pages

Scientific paper

In this paper, we prove that, if the coefficient f = f(t; y; z) of backward
doubly stochastic differential equations (BDSDEs for short) is assumed to be
continuous and linear growth in (y; z); then the uniqueness of solution and
continuous dependence with respect to the coefficients f, g and the terminal
value are equivalent.

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