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Stability of strong solutions of stochastic differential equations

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  • Slominski, Leszek

Abstract

For a sequence of stochastic differential equations of the type where [latin small letter f with hook] satisfies a Lipschitz condition, a stability theorem is presented under jointly weak convergence of driving processes . As a consequence the case of uniform convergence of and is discussed.

Suggested Citation

  • Slominski, Leszek, 1989. "Stability of strong solutions of stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 31(2), pages 173-202, April.
    • Handle: RePEc:eee:spapps:v:31:y:1989:i:2:p:173-202
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    Citations

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    Cited by:

    1. Aleksander Janicki & Zbigniew Michna & Aleksander Weron, 1996. "Approximation of stochastic differential equations driven by alpha-stable Levy motion," HSC Research Reports HSC/96/02, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    2. Rubenthaler, Sylvain, 2003. "Numerical simulation of the solution of a stochastic differential equation driven by a Lévy process," Stochastic Processes and their Applications, Elsevier, vol. 103(2), pages 311-349, February.
    3. Colino, Jesús P., 2008. "Weak convergence in credit risk," DES - Working Papers. Statistics and Econometrics. WS ws085518, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Yamada, Keigo, 1999. "Two limit theorems for queueing systems around the convergence of stochastic integrals with respect to renewal processes," Stochastic Processes and their Applications, Elsevier, vol. 80(1), pages 103-128, March.

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