Perturbations of generalized Mehler semigroups and applications to stochastic heat equations with Levy noise and singular drift

Lescot P, Röckner M (2004)
Potential Analysis 20(4): 317-344.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
In this paper we solve the Kolmogorov equation and, as a consequence, the martingale problem corresponding to a stochastic differential equation of type dX(t) = AX(t) dt + b(X-t) dt + dY(t), on a Hilbert space E, where (Y-t)(tgreater than or equal to0) is a Levy process on E, A generates a C-0-semigroup on E and b : E --> E. Our main point is to allow unbounded A and also singular (in particular, non-continuous) b. Our approach is based on perturbation theory of C-0-semigroups, which we apply to generalized Mehler semigroups considered on L-2(mu), where mu is their respective invariant measure. We apply our results, in particular, to stochastic heat equations with Levy noise and singular drift.
Erscheinungsjahr
Zeitschriftentitel
Potential Analysis
Band
20
Ausgabe
4
Seite(n)
317-344
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Lescot P, Röckner M. Perturbations of generalized Mehler semigroups and applications to stochastic heat equations with Levy noise and singular drift. Potential Analysis. 2004;20(4):317-344.
Lescot, P., & Röckner, M. (2004). Perturbations of generalized Mehler semigroups and applications to stochastic heat equations with Levy noise and singular drift. Potential Analysis, 20(4), 317-344. doi:10.1023/B:POTA.0000009814.54278.34
Lescot, P., and Röckner, M. (2004). Perturbations of generalized Mehler semigroups and applications to stochastic heat equations with Levy noise and singular drift. Potential Analysis 20, 317-344.
Lescot, P., & Röckner, M., 2004. Perturbations of generalized Mehler semigroups and applications to stochastic heat equations with Levy noise and singular drift. Potential Analysis, 20(4), p 317-344.
P. Lescot and M. Röckner, “Perturbations of generalized Mehler semigroups and applications to stochastic heat equations with Levy noise and singular drift”, Potential Analysis, vol. 20, 2004, pp. 317-344.
Lescot, P., Röckner, M.: Perturbations of generalized Mehler semigroups and applications to stochastic heat equations with Levy noise and singular drift. Potential Analysis. 20, 317-344 (2004).
Lescot, Paul, and Röckner, Michael. “Perturbations of generalized Mehler semigroups and applications to stochastic heat equations with Levy noise and singular drift”. Potential Analysis 20.4 (2004): 317-344.