Acta Mathematica Scientia

, Volume 39, Issue 3, pp 819–844 | Cite as

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 SyllaEmail author


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 

2010 MR Subject Classification

35D40 35R09 60H30 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Barles G, Buckdahn R, Pardoux E. Backward stochastic differential equations and integral-partial differential equations. Stochastics: An International Journal of Probability and Stochastic Processes, 1997, 60: 57–83MathSciNetzbMATHGoogle Scholar
  2. [2]
    Fujiwara T, Kunita H. Stochastic differential equations of jump type and Lévy processes in differomorphism group. J Math Kyoto Univ, 1985, 25(1): 71–106MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Hamadene S. Viscosity solutions of second order integral-partial differential equations without monotonicity condition: A new result. Nonlinear Analysis, 2016, 147: 213–235MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    Hamadène S, Morlais M -A. Viscosity solutions for second order integro-differential equations without monotonicity condition: The probabilistic Approach. Stochastics, 2016, 88(4): 632–649MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    Hamadène S, Ouknine Y. Reflected backward stochastic differential equation with jumps and random obstacle. Electron J Probab, 2003, 8(2): 1–20MathSciNetzbMATHGoogle Scholar
  6. [6]
    Harraj N, Ouknine Y, Turpin I. Double barriers Reflected BSDEs with jumps and viscosity solutions of parabolic Integro-differential PDEs. J Appl Math Stoch Anal, 2005, 1: 37–53CrossRefzbMATHGoogle Scholar
  7. [7]
    Lenglart E, Lépingle D, Pratelli M. Présentation unifiée de certaines inégalités de la théorie des martingales. Séminaire de probabilités (Strasbourg), tome, 1980, 14: 26–48zbMATHGoogle Scholar

Copyright information

© Wuhan Institute Physics and Mathematics, Chinese Academy of Sciences 2019

Authors and Affiliations

  1. 1.LERSTAD, CEAMITICUniversité Gaston BergerSaint-LouisSenegal

Personalised recommendations