Lp-solution of backward doubly stochastic differential equations

2009/07/11 by Auguste Aman, Aman, Auguste · 1 citation
Economics, Econometrics and Finance · Social Sciences · #60H05 #60H20 #FOS: Mathematics #Financial Risk and Volatility Modeling #Insurance, Mortality, Demography, Risk Management #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0907.1983

openalex publication_date 2009/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, our goal is solving backward doubly stochastic differential equation (BDSDE for short) under weak assumptions on the data. The first part of the paper is devoted to the development of some new technical aspects of stochastic calculus related to BDSDEs. Then we derive a priori estimates and prove existence and uniqueness of solutions, extending the results of Pardoux and Peng \citePP1 to the case where the solution is taked in L^p, p>1 and the monotonicity conditions are satisfied. This study is limited to deterministic terminal time.

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• L^p-solutions of Reflected Backward Doubly Stochastic Differential Equations

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