Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise

Marinelli C, Prévôt C, Röckner M (2010)
Journal of Functional Analysis 258(2): 616-649.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We prove existence, uniqueness and Lipschitz dependence on the initial datum for mild solutions of stochastic partial differential equations with Lipschitz coefficients driven by Wiener and Poisson noise. Under additional assumptions, we prove Gateaux and Frechet differentiability of solutions with respect to the initial datum. As an application, we obtain gradient estimates for the resolvent associated to the mild solution. Finally, we prove the strong Feller property of the associated semigroup. (C) 2009 Elsevier Inc. All rights reserved.
Erscheinungsjahr
Zeitschriftentitel
Journal of Functional Analysis
Band
258
Ausgabe
2
Seite(n)
616-649
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PUB-ID

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Marinelli C, Prévôt C, Röckner M. Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise. Journal of Functional Analysis. 2010;258(2):616-649.
Marinelli, C., Prévôt, C., & Röckner, M. (2010). Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise. Journal of Functional Analysis, 258(2), 616-649. doi:10.1016/j.jfa.2009.04.015
Marinelli, C., Prévôt, C., and Röckner, M. (2010). Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise. Journal of Functional Analysis 258, 616-649.
Marinelli, C., Prévôt, C., & Röckner, M., 2010. Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise. Journal of Functional Analysis, 258(2), p 616-649.
C. Marinelli, C. Prévôt, and M. Röckner, “Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise”, Journal of Functional Analysis, vol. 258, 2010, pp. 616-649.
Marinelli, C., Prévôt, C., Röckner, M.: Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise. Journal of Functional Analysis. 258, 616-649 (2010).
Marinelli, Carlo, Prévôt, Claudia, and Röckner, Michael. “Regular dependence on initial data for stochastic evolution equations with multiplicative Poisson noise”. Journal of Functional Analysis 258.2 (2010): 616-649.