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Empirical regression method for backward doubly stochastic differential equations. (English) Zbl 1345.60067

Summary: In this paper, we design a numerical scheme for approximating backward doubly stochastic differential equations which represent a solution to stochastic partial differential equations. We first use a time discretization and then we decompose the value function on a functions basis. The functions are deterministic and depend only on the time-space variables, while the decomposition coefficients depend on the external Brownian motion \(B\). The coefficients are evaluated through an empirical regression scheme, which is performed conditionally to \(B\). We establish nonasymptotic error estimates, conditionally to \(B\), and deduce how to tune parameters to obtain a convergence conditionally and unconditionally to \(B\). We provide numerical experiments as well.

MSC:

60H35 Computational methods for stochastic equations (aspects of stochastic analysis)
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
62G08 Nonparametric regression and quantile regression
65C30 Numerical solutions to stochastic differential and integral equations
90C39 Dynamic programming
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References:

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