Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations - Archive ouverte HAL
Journal Articles Journal of Stochastic Analysis Year : 2022

Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations

Abstract

We discuss a class of Backward Stochastic Differential Equations (BSDEs) with no driving martingale. When the randomness of the driver depends on a general Markov process $X$, those BSDEs are denominated Markovian BSDEs and can be associated to a deterministic problem, called Pseudo-PDE which constitute the natural generalization of a parabolic semilinear PDE which naturally appears when the underlying filtration is Brownian. We consider two aspects of well-posedness for the Pseudo-PDEs: "classical" and "martingale" solutions.
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Dates and versions

hal-01431559 , version 1 (11-01-2017)
hal-01431559 , version 2 (07-03-2017)
hal-01431559 , version 3 (24-12-2017)

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Adrien Barrasso, Francesco Russo. Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations. Journal of Stochastic Analysis , 2022, 3 (1), ⟨10.31390/josa.3.1.03⟩. ⟨hal-01431559v3⟩
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