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Stability in of martingales and backward equations under discretization of filtration

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  • Coquet, François
  • Mackevicius, Vigirdas
  • Mémin, Jean

Abstract

We consider a càdlàg process the filtration generated by Y and generated by step processes Yn defined from Y by discretization in time. We study the stability in (with Skorokhod topology) of -martingales and of -solutions of related backward equations, when Yn-->Y. We get this stability (in law) when Y is Markov and (in probability) under stronger assumptions on the coefficients of equations.

Suggested Citation

  • Coquet, François & Mackevicius, Vigirdas & Mémin, Jean, 1998. "Stability in of martingales and backward equations under discretization of filtration," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 235-248, July.
    • Handle: RePEc:eee:spapps:v:75:y:1998:i:2:p:235-248
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    References listed on IDEAS

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    1. Antonelli, Fabio, 1996. "Stability of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 103-114, March.
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    Cited by:

    1. Kraft, Holger & Seifried, Frank Thomas, 2014. "Stochastic differential utility as the continuous-time limit of recursive utility," Journal of Economic Theory, Elsevier, vol. 151(C), pages 528-550.
    2. Crisan, D. & Manolarakis, K. & Touzi, N., 2010. "On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1133-1158, July.
    3. Coquet, François & Mackevicius, Vigirdas & Mémin, Jean, 1999. "Corrigendum to "Stability in of martingales and backward equations under discretization of filtration": [Stochastic Processes and their Applications 75 (1998) 235-248]," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 335-338, August.
    4. Bouchard, Bruno & Touzi, Nizar, 2004. "Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 111(2), pages 175-206, June.

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