Ergodic BSDE with unbounded and multiplicative underlying diffusion and application to large time behaviour of viscosity solution of HJB equation

Ying Hu and Florian Lemonnier

Stochastic Processes and their Applications, 2019, vol. 129, issue 10, 4009-4050

Abstract: We study ergodic backward stochastic differential equations (EBSDEs), for which the underlying diffusion is assumed to be multiplicative and of linear growth. The fact that the forward process has an unbounded diffusion is balanced with an assumption of weak dissipativity for its drift. Moreover, the forward equation is assumed to be non-degenerate. We study the existence and uniqueness of EBSDEs and we apply our results to an ergodic optimal control problem. In particular, we show the large time behaviour of viscosity solution of Hamilton–Jacobi–Bellman equation with an exponential rate of convergence when the underlying diffusion is multiplicative and unbounded.

Keywords: Multiplicative and unbounded diffusion; Ergodic backward stochastic differential equation; HJB equation; Large time behaviour; Rate of convergence (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.11.008

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