Ergodic BSDEs driven by G-Brownian motion and applications

Mingshang Hu · Falei Wang

17 citations0/0 files storedStochastics and Dynamics

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Stochastic processes and financial applications Nonlinear Partial Differential Equations Fuzzy Systems and Optimization

Abstract

This paper considers a new kind of backward stochastic differential equations (BSDEs) driven by [Formula: see text]-Brownian motion, which is called ergodic [Formula: see text]-BSDEs. Firstly, the well-posedness of [Formula: see text]-BSDEs with infinite horizon is given by combining a new linearization method with the argument of Briand and Hu [4]. Then, in view of [Formula: see text]-stochastic calculus approach the Feynman–Kac formula for fully nonlinear elliptic partial differential equations (PDEs) is established. Finally, with the help of the aforementioned results we obtain the existence of solution to [Formula: see text]-EBSDE and some applications are also stated.

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References

1990Adapted solution of a backward stochastic differential equation 1997Backward Stochastic Differential Equations in Finance 2005Backward stochastic differential equations and quasilinear parabolic partial differential equations 2019Nonlinear Expectations and Stochastic Calculus under Uncertainty 2007G-Expectation, G-Brownian Motion and Related Stochastic Calculus of Itô Type 2010Function Spaces and Capacity Related to a Sublinear Expectation: Application to G-Brownian Motion Paths 2008Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation 1991Probabilistic interpretation for systems of quasilinear parabolic partial differential equations

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2019Multi-dimensional BSDEs driven by G-Brownian motion and related system of fully nonlinear PDEs

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