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Stochastics
An International Journal of Probability and Stochastic Processes
Volume 88, 2016 - Issue 6
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Articles

Malliavin calculus for Markov chains using perturbations of time

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Pages 813-840 | Received 23 Dec 2014, Accepted 26 Jan 2016, Published online: 19 Feb 2016

References

  • V. Bally and E. Clément, Integration by parts formula with respect to jump times for stochastic differential equations, in Stochastic Analysis, Springer Verlag, Berlin Heidelberg, 2010.
  • K. Bichteler, J.B. Gravereaux, and J. Jacod, Malliavin Calculus for Processes with Jumps, Gordon and Breach Science, Amsterdam, 1987.
  • N. Bouleau, Error Calculus for Finance and Physics, the Language of Dirichlet Forms, De Gruyter, Berlin, 2003.
  • N. Bouleau and L. Denis, Energy image density property and the lent particle method for Poisson measures, J. Funct. Anal. 257(4) (2009), pp. 1144–1174.
  • N. Bouleau and L. Denis, Dirichlet Forms Methods for Poisson Point Measures and Lévy Processes, Probability Theory and Stochastic Modeling Vol. 76, Springer, Cham, 2016.
  • N. Bouleau and F. Hirsch, Formes de Dirichlet générales et densité des variables aléatoires réelles sur l’espace de Wiener, J. Funct. Anal. 69(2) (1986), pp. 229–259.
  • N. Bouleau and F. Hirsch, Dirichlet Forms and Analysis on Wiener Space, De Gruyter, Berlin, 1991.
  • E.A. Carlen and E. Pardoux, Differential calculus and integration by parts on Poisson space, in Stochastics, Algebra and Ananlysis in Classical and Quantum Dynamics, Kluwer, Albeverio, Sergio, Blanchard, Philip, Testard, D., eds., Academic Publishers, Dordrecht, 1990, pp. 63–73.
  • A. Coquio, Formes de Dirichlet sur l’espace canonique de Poisson et application aux équations différentielles stochastiques, Ann. Inst. Henri Poincaré 19(1) (1993), pp. 1–36.
  • L. Denis, A criterion of density for solutions of Poisson-driven SDEs, Probab. Theory Relat. Fields 118 (2000), pp. 406–426.
  • Y. El-Khatib and N. Privault, Computations of Greeks in a market with jumps via the Malliavin calculus, Finance Stoch. 8(2) (2004), pp. 161–179.
  • Y. Ishikawa and H. Kunita, Malliavin calculus on the Wiener--Poisson space and its application to canonical SDE with jumps, Stoch. Process. Appl. 116 (2006), pp. 1743–1769.
  • J. Jacod, Calcul Stochastique et Problème de Martingales, Lecture Notes in Mathematics Vol. 714, Springer, Berlin Heidelberg, 1979.
  • R. Kawai and A. Takeuchi, Greeks formulas for an asset price model with gamma process, Math. Finance 21(4) (2011), pp. 723–742.
  • Z.M. Ma and M. Röckner, Construction of diffusion on configuration spaces, Osaka J. Math. 37 (2000), pp. 273–314.
  • I. Nourdin and T. Simon, On the absolute continuity of Lévy processes with drift, Ann. Probab. 34 (2006), pp. 1035–1051.
  • D. Nualart and J. Vives, Anticipative calculus for the Poisson process based on the Fock space, Séminaire de Probabilit\’{e}s XXIV, Lecture Notes in Mathematics Vol. 1426, Springer-Verlag, Berlin Heidelberg, 1990.
  • J. Picard, On the existence of smooth densities for jump processes, Probab. Theory Relat. Fields 105 (1996), pp. 481–511.
  • N. Privault, Stochastic Analysis in Discrete and Continuous Settings, Lecture Notes in Mathematics, Springer-Verlag, Berlin Heidelberg, 2009.

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