A probabilistic approach to large time behaviour of mild solutions of Hamilton-Jacobi-Bellman equations in infinite dimension

Ying Hu; Pierre-Yves Madec; Adrien Richou

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arXiv · 1406.5993

A probabilistic approach to large time behaviour of mild solutions of Hamilton-Jacobi-Bellman equations in infinite dimension

Ying Hu·Pierre-Yves Madec·Adrien Richou

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Abstract

We study the large time behaviour of mild solutions of HJB equations in infinite dimension by a purely probabilistic approach. For that purpose, we show that the solution of a BSDE in finite horizon $T$ taken at initial time behaves like a linear term in $T$ shifted with the solution of the associated EBSDE taken at initial time. Moreover we give an explicit speed of convergence, which seems to appear very rarely in literature.

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Ying Hu, Pierre-Yves Madec, Adrien Richou. 2014-06-23. A probabilistic approach to large time behaviour of mild solutions of Hamilton-Jacobi-Bellman equations in infinite dimension. https://arxiv.org/abs/1406.5993

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