### Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities

Gordina M, Röckner M, Teplyaev A (2020)
Probability Theory and Related Fields.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch

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Autor*in
Gordina, Maria; Röckner, MichaelUniBi; Teplyaev, Alexander
Einrichtung
Abstract / Bemerkung
We consider a perturbation of a Hilbert space-valued Ornstein-Uhlenbeck process by a class of singular nonlinear non-autonomous maximal monotone time-dependent drifts. The only further assumption on the drift is that it is bounded on balls in the Hilbert space uniformly in time. First we introduce a new notion of generalized solutions for such equations which we call pseudo-weak solutions and prove that they always exist and obtain pathwise estimates in terms of the data of the equation. Then we prove that their laws are absolutely continuous with respect to the law of the original Ornstein-Uhlenbeck process. In particular, we show that pseudo-weak solutions always have continuous sample paths. In addition, we obtain integrability estimates of the associated Girsanov densities. Some of our results concern non-random equations as well, while probabilistic results are new even in finite-dimensional autonomous settings.
Stichworte
Ornstein-Uhlenbeck process; Singular perturbation; Nonlinear; infinite-dimensional stochastic differential equations; Non-Lipschitz; monotone coefficients; Girsanov theorem
Erscheinungsjahr
2020
Zeitschriftentitel
Probability Theory and Related Fields
ISSN
0178-8051
eISSN
1432-2064
Page URI
https://pub.uni-bielefeld.de/record/2945609

### Zitieren

Gordina M, Röckner M, Teplyaev A. Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities. Probability Theory and Related Fields. 2020.
Gordina, M., Röckner, M., & Teplyaev, A. (2020). Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities. Probability Theory and Related Fields. doi:10.1007/s00440-020-00991-w
Gordina, M., Röckner, M., and Teplyaev, A. (2020). Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities. Probability Theory and Related Fields.
Gordina, M., Röckner, M., & Teplyaev, A., 2020. Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities. Probability Theory and Related Fields.
M. Gordina, M. Röckner, and A. Teplyaev, “Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities”, Probability Theory and Related Fields, 2020.
Gordina, M., Röckner, M., Teplyaev, A.: Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities. Probability Theory and Related Fields. (2020).
Gordina, Maria, Röckner, Michael, and Teplyaev, Alexander. “Ornstein-Uhlenbeck processes with singular drifts: integral estimates and Girsanov densities”. Probability Theory and Related Fields (2020).

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