Nonlinear Fractional Backward Doubly Stochastic Differential Equations with Hurst Parameter in (1/2,1)

Details Nonlinear Fractional Backward Doubly Stochastic Differential Equations with Hurst Parameter in (1/2,1) Nonlinear Fractional Backward Doubly Stochastic Differential Equations with Hurst Parameter in (1/2,1)

2011-03-17

arxiv.org/abs/1103.3366v1

Mathematics

Probability

17 pages

Scientific paper

We first state a special type of It\^o formula involving stochastic integrals of both standard and fractional Brownian motions. Then we use Doss-Sussman transformation to establish the link between backward doubly stochastic differential equations, driven by both standard and fractional Brownian motions, and backward stochastic differential equations, driven only by standard Brownian motions. Following the same technique, we further study associated nonlinear stochastic partial differential equations driven by fractional Brownian motions and partial differential equations with stochastic coefficients.

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