Lp solutions of backward stochastic differential equations

Briand, Philippe; Delyon, Bernard; Hu, Ying; Pardoux, Étienne; Stoica, Lucreţiu

doi:10.1016/s0304-4149(03)00089-9

Cited by 319 publications

(366 citation statements)

References 6 publications

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“…Later, Briand et al [14] found that the polynomial growth condition is not necessary if one uses the monotonicity condition similar to that of [63].…”

Section: Introductionmentioning

confidence: 99%

Lp solutions of backward stochastic differential equations with jumps

Yao

2017

Stochastic Processes and their Applications

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Given p ∈ (1, 2), we study L p solutions of a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) whose generator may not be Lipschitz continuous in (y, z)−variables. We show that such a BSDEJ with p−integrable terminal data admits a unique L p solution by approximating the monotonic generator by a sequence of Lipschitz generators via convolution with mollifiers and using a stability result.

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“…Later, Briand et al [14] found that the polynomial growth condition is not necessary if one uses the monotonicity condition similar to that of [63].…”

Section: Introductionmentioning

confidence: 99%

Lp solutions of backward stochastic differential equations with jumps

Yao

2017

Stochastic Processes and their Applications

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“…Even though there exist some improvements of Pardoux-Peng's result for multidimensional BSDEs (see e.g. [3,13] ), the case of real valued BSDEs meaning that Y is a real process is easier to handle. The main reason for the gap between the real case and the multidimensional one comes from the comparison theorem which turns out to be a powerful tool to construct solutions for real valued BSDEs.…”

Section: Introductionmentioning

confidence: 99%

Quadratic BSDEs with convex generators and unbounded terminal conditions

Briand

2007

Probab. Theory Relat. Fields

240

276

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In a previous work, we proved an existence result for BSDEs with quadratic generators with respect to the variable z and with unbounded terminal conditions. However, no uniqueness result was stated in that work. The main goal of this paper is to fill this gap. In order to obtain a comparison theorem for this kind of BSDEs, we assume that the generator is convex with respect to the variable z. Under this assumption of convexity, we are also able to prove a stability result in the spirit of the a priori estimates stated in the article of N. El Karoui, S. Peng and M.-C. Quenez. With these tools in hands, we can derive the nonlinear Feynman--Kac formula in this context

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“…Hence there exists a continuous processỸ ∈ Class (D) such that lim N→∞ ||Ỹ N −Ỹ || 1 = 0. For any 0 < β < 1, using Lemma 6.1 in [4] and (3.34) we get …”

Section: Theorem 32 Assumementioning

confidence: 93%

“…We have to work in the framework of L 1 and deal with class D stochastic processes. We refer the readers to the nice article [4] for related results.…”

Section: Q(x(s))ds ϕ(X τ D )]mentioning

confidence: 99%

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Backward Stochastic Differential Equations and Dirichlet Problems of Semilinear Elliptic Operators with Singular Coefficients

Yang

Zhang

2017

Potential Anal

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In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic differential operators which do not necessarily have the maximum principle and are non-symmetric in general. Our method is probabilistic. It turns out that we need to solve a class of backward stochastic differential equations with singular coefficients, which is of independent interest itself. The theory of Dirichlet forms also plays an important role.Keywords Dirichlet boundary value problem · Semilinear second order elliptic differential equations · Dirichlet forms · Backward stochastic differential equations Mathematics Subject Classifications (2010) Primary 60H60 · Secondary 60H30, 31J25

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Lp solutions of backward stochastic differential equations

Cited by 319 publications

References 6 publications

Lp solutions of backward stochastic differential equations with jumps

Lp solutions of backward stochastic differential equations with jumps

Quadratic BSDEs with convex generators and unbounded terminal conditions

Backward Stochastic Differential Equations and Dirichlet Problems of Semilinear Elliptic Operators with Singular Coefficients

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