Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces

Bogachev V, Da Prato G, Röckner M (2010)
Journal of Evolution Equations 10(3): 487-509.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Bogachev, Vladimir; Da Prato, Giuseppe; Röckner, MichaelUniBi
Abstract / Bemerkung
We consider a stochastic differential equation in a Hilbert space with time-dependent coefficients for which no general existence and uniqueness results are known. We prove, under suitable assumptions, the existence and uniqueness of a measure valued solution, for the corresponding Fokker-Planck equation. In particular, we verify the Chapman-Kolmogorov equations and get an evolution system of transition probabilities for the stochastic dynamics informally given by the stochastic differential equation.
Stichworte
stochastic PDEs; measures; Fokker-Planck equations; Kolmogorov operators; parabolic equations for
Erscheinungsjahr
2010
Zeitschriftentitel
Journal of Evolution Equations
Band
10
Ausgabe
3
Seite(n)
487-509
ISSN
1424-3199
Page URI
https://pub.uni-bielefeld.de/record/1794324

Zitieren

Bogachev V, Da Prato G, Röckner M. Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces. Journal of Evolution Equations. 2010;10(3):487-509.
Bogachev, V., Da Prato, G., & Röckner, M. (2010). Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces. Journal of Evolution Equations, 10(3), 487-509. doi:10.1007/s00028-010-0058-y
Bogachev, V., Da Prato, G., and Röckner, M. (2010). Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces. Journal of Evolution Equations 10, 487-509.
Bogachev, V., Da Prato, G., & Röckner, M., 2010. Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces. Journal of Evolution Equations, 10(3), p 487-509.
V. Bogachev, G. Da Prato, and M. Röckner, “Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces”, Journal of Evolution Equations, vol. 10, 2010, pp. 487-509.
Bogachev, V., Da Prato, G., Röckner, M.: Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces. Journal of Evolution Equations. 10, 487-509 (2010).
Bogachev, Vladimir, Da Prato, Giuseppe, and Röckner, Michael. “Existence and uniqueness of solutions for Fokker-Planck equations on Hilbert spaces”. Journal of Evolution Equations 10.3 (2010): 487-509.

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