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Time Reversal of Solutions of Equations Driven by Lévy Processes

  • P. Sundar
Part of the Progress in Probability book series (PRPR, volume 27)

Abstract

Time reversal of solutions of stochastic differential equations driven by Lévy processes is shown under suitable hypotheses. Possible weakening of the sufficient conditions for time reversal is briefly discussed.

Keywords

Stochastic Differential Equation Time Reversal Markov Property Poisson Random Measure Stochastic Flow 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    K. Bichteler, J-B. Gravereaux and J. Jacod (1987): Malliavin Calculus for processes with jumps. Stochastics Monographs. Gordon and Breach Science Publishers.Google Scholar
  2. [2]
    M. Emery (1982): En marge de l’exposé de Meyer: “Geométrie differéntielle stochastique”. Springer-Verlag Lecture Notes in Math. 921, 208–216.Google Scholar
  3. [3]
    K. Itô (1978): Extension of stochastic integrals. Proc. Int. Symp. SDE’s. Wiley, New York.Google Scholar
  4. [4]
    J. Jacod (1979): Calcul stochastique et Problemes de martingales. Springer-Verlag Lecture Notes in Math. 714.Google Scholar
  5. [5]
    J. Jacod (1985): Grossissement initial, hypothese (H’), et théorème de Girsanov. Springer-Verlag Lecture Notes in Math., 1118, 15–35.Google Scholar
  6. [6]
    J. Jacod and Ph.E. Protter (1988): Time reversal on Lévy processes. Ann. Probab. 16, 620–641.MathSciNetMATHCrossRefGoogle Scholar
  7. [8]
    P.A. Meyer (1981): Flot d’une equation differentielle stochastique. Springer-Verlag Lecture Notes in Math. 850, 103–117.Google Scholar
  8. [9]
    R. Leandre (1984): Flot d’une equation differentielle stochastique avec semi-martingales disectrice discontinue. Springer-Verlag Lecture Notes in Math. 1123, 271–275.Google Scholar
  9. [10]
    E. Pardoux (1986): Grossissement d’une filtration et retournement du temps d’une diffusion. Springer-Verlag Lecture Notes in Math. 1204, 48–56.Google Scholar
  10. [11]
    P. Sundar (1989): Invertibility of stochastic flows and time reversal of solutions of SDE’s driven by Lévy processes with bounded jumps. Soochow J.Math. 15, 193–204.MathSciNetMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • P. Sundar
    • 1
  1. 1.Department of MathematicsLouisiana State UniversityBaton Rouge

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