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2015 Existence and uniqueness for backward stochastic differential equations driven by a random measure, possibly non quasi-left continuous
Elena Bandini
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Electron. Commun. Probab. 20: 1-13 (2015). DOI: 10.1214/ECP.v20-4348

Abstract

We study the following backward stochastic differential equation on finite time horizon driven by an integer-valued random measure $\mu$ on $\mathbb R_+\times E$, where $E$ is a Lusin space, with compensator $\nu(dt,dx)=dA_t\,\phi_t(dx)$:\[Y_t = \xi + \int_{(t,T]} f(s,Y_{s-},Z_s(\cdot))\, d A_s - \int_{(t,T]} \int_E Z_s(x) \, (\mu-\nu)(ds,dx),\qquad 0\leq t\leq T.\]The generator $f$ satisfies, as usual, a uniform Lipschitz condition with respect to its last two arguments. In the literature, the existence and uniqueness for the above equation in the present general setting has only been established when $A$ is continuous or deterministic. The general case, i.e. $A$ is a right-continuous nondecreasing predictable process, is addressed in this paper.

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Elena Bandini. "Existence and uniqueness for backward stochastic differential equations driven by a random measure, possibly non quasi-left continuous." Electron. Commun. Probab. 20 1 - 13, 2015. https://doi.org/10.1214/ECP.v20-4348

Information

Accepted: 6 October 2015; Published: 2015
First available in Project Euclid: 7 June 2016

zbMATH: 1329.60172
MathSciNet: MR3407215
Digital Object Identifier: 10.1214/ECP.v20-4348

Subjects:
Primary: 60H10
Secondary: 60G57

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