A MILD ITO FORMULA FOR SPDES

Da Prato G, Jentzen A, Röckner M (2019)
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 372(6): 3755-3807.

Zeitschriftenaufsatz | Veröffentlicht| Englisch
 
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Abstract / Bemerkung
This article introduces a certain class of stochastic processes, which we suggest calling mild Ito processes, and a new, somehow mild, Ito-type formula for such processes. Examples of mild Ito processes are mild solutions of stochastic partial differential equations (SPDEs) and their numerical approximation processes. We illustrate the capacity of the mild Ito formula by several applications. In particular, we illustrate how the mild Ito formula can be used to derive improved a priori bounds for SPDEs, we demonstrate how the mild Ito formula can be employed to establish improved Holder continuity properties for solutions of Kolmogorov partial differential equations (PDEs) in Hilbert spaces, and we illustrate how the mild Ito formula can be used to solve the weak convergence problem for numerical approximations of SPDEs with nonlinear diffusion coefficients.
Erscheinungsjahr
2019
Zeitschriftentitel
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Band
372
Ausgabe
6
Seite(n)
3755-3807
ISSN
0002-9947
eISSN
1088-6850
Page URI
https://pub.uni-bielefeld.de/record/2937858

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Da Prato G, Jentzen A, Röckner M. A MILD ITO FORMULA FOR SPDES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 2019;372(6):3755-3807.
Da Prato, G., Jentzen, A., & Röckner, M. (2019). A MILD ITO FORMULA FOR SPDES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 372(6), 3755-3807. doi:10.1090/tran/7165
Da Prato, G., Jentzen, A., and Röckner, M. (2019). A MILD ITO FORMULA FOR SPDES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 372, 3755-3807.
Da Prato, G., Jentzen, A., & Röckner, M., 2019. A MILD ITO FORMULA FOR SPDES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 372(6), p 3755-3807.
G. Da Prato, A. Jentzen, and M. Röckner, “A MILD ITO FORMULA FOR SPDES”, TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, vol. 372, 2019, pp. 3755-3807.
Da Prato, G., Jentzen, A., Röckner, M.: A MILD ITO FORMULA FOR SPDES. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 372, 3755-3807 (2019).
Da Prato, Giuseppe, Jentzen, Arnulf, and Röckner, Michael. “A MILD ITO FORMULA FOR SPDES”. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 372.6 (2019): 3755-3807.