REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH JUMPS AND VISCOSITY SOLUTION OF SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITHOUT MONOTONICITY CONDITION: CASE WITH THE MEASURE OF LÉVY INFINITE

doi:10.1007/s10473-019-0312-5

数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (3): 819-844.doi: 10.1007/s10473-019-0312-5

REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH JUMPS AND VISCOSITY SOLUTION OF SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITHOUT MONOTONICITY CONDITION: CASE WITH THE MEASURE OF LÉVY INFINITE

Lamine SYLLA

Université Gaston Berger, LERSTAD, CEAMITIC, Senegal

收稿日期:2018-01-03 出版日期:2019-06-25 发布日期:2019-06-27
作者简介:Lamine SYLLA,E-mail:sylla.lamine@ugb.edu.sn

REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH JUMPS AND VISCOSITY SOLUTION OF SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITHOUT MONOTONICITY CONDITION: CASE WITH THE MEASURE OF LÉVY INFINITE

Lamine SYLLA

Université Gaston Berger, LERSTAD, CEAMITIC, Senegal

Received:2018-01-03 Online:2019-06-25 Published:2019-06-27

摘要/Abstract

摘要： We consider the problem of viscosity solution of integro-partial differential equation(IPDE in short) with one obstacle via the solution of reflected backward stochastic differential equations(RBSDE in short) with jumps. We show the existence and uniqueness of a continuous viscosity solution of equation with non local terms, if the generator is not monotonous and Levy's measure is infinite.

关键词: Integro-partial differential equation, reflected stochastic differential equations with jumps, viscosity solution, non-local operator

Abstract: We consider the problem of viscosity solution of integro-partial differential equation(IPDE in short) with one obstacle via the solution of reflected backward stochastic differential equations(RBSDE in short) with jumps. We show the existence and uniqueness of a continuous viscosity solution of equation with non local terms, if the generator is not monotonous and Levy's measure is infinite.

Key words: Integro-partial differential equation, reflected stochastic differential equations with jumps, viscosity solution, non-local operator

中图分类号:

35D40

Lamine SYLLA. REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH JUMPS AND VISCOSITY SOLUTION OF SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITHOUT MONOTONICITY CONDITION: CASE WITH THE MEASURE OF LÉVY INFINITE[J]. 数学物理学报(英文版), 2019, 39(3): 819-844.

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REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH JUMPS AND VISCOSITY SOLUTION OF SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITHOUT MONOTONICITY CONDITION: CASE WITH THE MEASURE OF LÉVY INFINITE

REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH JUMPS AND VISCOSITY SOLUTION OF SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITHOUT MONOTONICITY CONDITION: CASE WITH THE MEASURE OF LÉVY INFINITE

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