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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Submitted on : Sunday, December 24, 2017 - 8:03:34 AM
Last modification on : Wednesday, January 23, 2019 - 10:29:31 AM

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  • HAL Id : hal-01431559, version 3
  • ARXIV : 1701.02899

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Adrien Barrasso, Francesco Russo. Backward Stochastic Differential Equations with no driving martingale, Markov processes and associated Pseudo Partial Differential Equations. 2017. 〈hal-01431559v3〉

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