Reflected backward doubly stochastic differential equations driven by a Lévy process with stochastic Lipschitz condition

Hu, Lan-Ying

doi:10.1016/j.amc.2012.07.023

Cited by 5 publications

(4 citation statements)

References 3 publications

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“…By the definition of f n , Lemma 2.3, and Lemma 2.4, we can easily deduce BDSDEs(ξ, f n , g) is a special case in [8]. Therefore, BDSDEs(ξ, f n , g) have a unique solution denoted by (Y n t , Z n t ).…”

Section: Existence and Uniquenessmentioning

confidence: 94%

Multidimensional backward doubly stochastic differential equations with integral non-Lipschitz coefficients

Duan¹

2017

J. Nonlinear Sci. Appl.

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The paper is devoted to solve multidimensional backward doubly stochastic differential equations under integral nonLipschitz conditions in general spaces. By stochastic analysis and constructing approximation sequence, a new set of sufficient conditions for multidimensional backward doubly stochastic differential equations is obtained. The results generalize the recent results on this issue. Finally, an example is given to illustrate the advantage of the main results. c 2017 all rights reserved.

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Section: Existence and Uniquenessmentioning

confidence: 94%

Multidimensional backward doubly stochastic differential equations with integral non-Lipschitz coefficients

Duan¹

2017

J. Nonlinear Sci. Appl.

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“…Following this, Ren [36] has considered RBDSDEs driven by Teugels martingales associated with a Lévy process, in which the barrier process is right continuous with left limits. We stress that the theory of RBDSDEs has been extended to the case where the barrier is not necessarily continuous and/or a larger filtration than the Brownian filtration, or by weakening the assumptions on the coefficients, by several authors, we quote [3,5,2,18,22,36] and references therein. In all of the mentioned works, the barrier has been assumed to be at least right continuous.…”

Section: Introductionmentioning

confidence: 99%

Penalization method for reflected BDSDEs with two-sided jumps and driven by Lévy process

Marzougue¹

2021

Preprint

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“…To this direction, several attempts have been done. Among others, we refer to [4,5,9,15,[21][22][23][24] for the case of BSDEs, and [16,25,26,30] for BDSDEs. In our paper, we use a generalization of the Doob-Meyer decomposition called the Mertens decomposition.…”

Section: Introductionmentioning

confidence: 99%

“…To this direction, several attempts have been done. Among others, we refer to [4,5,9,15,[21][22][23][24] for the case of BSDEs, and [16,25,26,30] for BDSDEs.…”

Section: Introductionmentioning

confidence: 99%

Irregular barrier reflected BDSDEs with general jumps under stochastic Lipschitz and linear growth conditions

Marzougue¹,

Sagna²

2020

Modern Stochastics: Theory and Applications

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In this paper, a solution is given to reflected backward doubly stochastic differential equations when the barrier is not necessarily right-continuous, and the noise is driven by two independent Brownian motions and an independent Poisson random measure. The existence and uniqueness of the solution is shown, firstly when the coefficients are stochastic Lipschitz, and secondly by weakening the conditions on the stochastic growth coefficient.

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Reflected backward doubly stochastic differential equations driven by a Lévy process with stochastic Lipschitz condition

Cited by 5 publications

References 3 publications

Multidimensional backward doubly stochastic differential equations with integral non-Lipschitz coefficients

Multidimensional backward doubly stochastic differential equations with integral non-Lipschitz coefficients

Penalization method for reflected BDSDEs with two-sided jumps and driven by Lévy process

Irregular barrier reflected BDSDEs with general jumps under stochastic Lipschitz and linear growth conditions

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