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

Autor(en)
Lescot, Paul ; Röckner, Michael
Normierter Zeitschriftentitel
Potential analysis 
DOI
10.1023/B:POTA.0000009814.54278.34
ISSN
0926-2601
URL
https://pub.uni-bielefeld.de/record/1609133
Web of Science-ID
000187516500002

Weitere Details

Sprache
englisch
Darstellungsform
Text
Band
20
Ausgabe
4
Seitenbereich
317 - 344
Schlagwörter
equations , generalized Mehler semigroups , perturbation theory , stochastic heat

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.

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