# About the infinite dimensional skew and obliquely reflected Ornstein-Uhlenbeck process

Röckner M, Trutnau G (2016)
Infinite Dimensional Analysis Quantum Probability and Related Topics 18(4): 1550031.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
Based on an integration by parts formula for closed and convex subsets Gamma of a separable real Hilbert space H with respect to a Gaussian measure, we first construct and identify the infinite dimensional analogue of the obliquely reflected Ornstein-Uhlenbeck process (perturbed by a bounded drift B) by means of a Skorokhod type decomposition. The variable oblique reflection at a reflection point of the boundary. G is uniquely described through a reflection angle and a direction in the tangent space (more precisely through an element of the orthogonal complement of the normal vector) at the reflection point. In case of normal reflection at the boundary of a regular convex set and under some monotonicity condition on B, we prove the existence and uniqueness of a strong solution to the corresponding SDE. Subsequently, we consider an increasing sequence (Gamma(alpha k))(k) (is an element of Z) of closed and convex subsets of H and the skew reflection problem at the boundaries of this sequence. We present concrete examples and obtain as a special case the infinite dimensional analogue of the p-skew reflected Ornstein-Uhlenbeck process.
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Zeitschriftentitel
Infinite Dimensional Analysis Quantum Probability and Related Topics
Band
18
Ausgabe
4
Art.-Nr.
1550031
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Röckner M, Trutnau G. About the infinite dimensional skew and obliquely reflected Ornstein-Uhlenbeck process. Infinite Dimensional Analysis Quantum Probability and Related Topics. 2016;18(4): 1550031.
Röckner, M., & Trutnau, G. (2016). About the infinite dimensional skew and obliquely reflected Ornstein-Uhlenbeck process. Infinite Dimensional Analysis Quantum Probability and Related Topics, 18(4), 1550031. doi:10.1142/S0219025715500319
Röckner, M., and Trutnau, G. (2016). About the infinite dimensional skew and obliquely reflected Ornstein-Uhlenbeck process. Infinite Dimensional Analysis Quantum Probability and Related Topics 18:1550031.
Röckner, M., & Trutnau, G., 2016. About the infinite dimensional skew and obliquely reflected Ornstein-Uhlenbeck process. Infinite Dimensional Analysis Quantum Probability and Related Topics, 18(4): 1550031.
M. Röckner and G. Trutnau, “About the infinite dimensional skew and obliquely reflected Ornstein-Uhlenbeck process”, Infinite Dimensional Analysis Quantum Probability and Related Topics, vol. 18, 2016, : 1550031.
Röckner, M., Trutnau, G.: About the infinite dimensional skew and obliquely reflected Ornstein-Uhlenbeck process. Infinite Dimensional Analysis Quantum Probability and Related Topics. 18, : 1550031 (2016).
Röckner, Michael, and Trutnau, Gerald. “About the infinite dimensional skew and obliquely reflected Ornstein-Uhlenbeck process”. Infinite Dimensional Analysis Quantum Probability and Related Topics 18.4 (2016): 1550031.

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