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Journal Articles Stochastic Processes and their Applications Year : 2021

Martingale driven BSDEs, PDEs and other related deterministic problems

Abstract

We focus on a class of BSDEs driven by a cadlag martingale and corresponding Markov type BSDE which arise when the randomness of the driver appears through a Markov process. To those BSDEs we associate a deterministic problem which, when the Markov process is a Brownian diffusion, is nothing else but a parabolic type PDE. The solution of the deterministic problem is intended as decoupled mild solution, and it is formulated with the help of a time-inhomogeneous semigroup.
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Dates and versions

hal-01566883 , version 1 (21-07-2017)
hal-01566883 , version 2 (26-11-2020)

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Adrien Barrasso, Francesco Russo. Martingale driven BSDEs, PDEs and other related deterministic problems. Stochastic Processes and their Applications, 2021, 133, pp.193-228. ⟨10.1016/j.spa.2020.11.007⟩. ⟨hal-01566883v2⟩
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