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Ergodic BSDEs and related PDEs with Neumann boundary conditions under weak dissipative assumptions

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  • Madec, P.Y.

Abstract

We study a class of ergodic BSDEs related to PDEs with Neumann boundary conditions. The randomness of the driver is given by a forward process under weakly dissipative assumptions with an invertible and bounded diffusion matrix. Furthermore, this forward process is reflected in a convex subset of Rd not necessarily bounded. We study the link of such EBSDEs with PDEs and we apply our results to an ergodic optimal control problem.

Suggested Citation

  • Madec, P.Y., 2015. "Ergodic BSDEs and related PDEs with Neumann boundary conditions under weak dissipative assumptions," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1821-1860.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:5:p:1821-1860
    DOI: 10.1016/j.spa.2014.11.015
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    References listed on IDEAS

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    1. Debussche, Arnaud & Hu, Ying & Tessitore, Gianmario, 2011. "Ergodic BSDEs under weak dissipative assumptions," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 407-426, March.
    2. Richou, Adrien, 2009. "Ergodic BSDEs and related PDEs with Neumann boundary conditions," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2945-2969, September.
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    Cited by:

    1. Hu, Ying & Lemonnier, Florian, 2019. "Ergodic BSDE with unbounded and multiplicative underlying diffusion and application to large time behaviour of viscosity solution of HJB equation," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4009-4050.
    2. Wu, Hao & Li, Xuefeng, 2021. "Converse comparison theorems for multidimensional anticipated backward stochastic differential equations," Statistics & Probability Letters, Elsevier, vol. 168(C).

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