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

2011/03/17 by Shuai Jing, Jing, Shuai
Economics, Econometrics and Finance · Mathematics · #35R60 #60G22 #60H15 #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #math.PR #msc:35R60 #msc:60G22 #msc:60H15

paper · pdf · doi:10.48550/arxiv.1103.3366

17 pages

arxiv created 2011/03/17 · openalex publication_date 2011/03/17 · arxiv updated 2011/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We first state a special type of Itô 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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