STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS

Röckner M, Wu B, Zhu R, Zhu X (2020)
SIAM JOURNAL ON MATHEMATICAL ANALYSIS 52(3): 2237-2274.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Röckner, MichaelUniBi; Wu, Bo; Zhu, RongchanUniBi; Zhu, Xiangchan
Abstract / Bemerkung
In this paper, we prove the existence of martingale solutions to the stochastic heat equation taking values in a Riemannian manifold, which admits the Wiener (Brownian bridge) measure on the Riemannian path (loop) space as an invariant measure using a suitable Dirichlet form. Using the Andersson-Driver approximation, we heuristically derive a form of the equation solved by the process given by the Dirichlet form. Moreover, we establish the log-Sobolev inequality for the Dirichlet form in the path space. In addition, some characterizations for the lower bound of the Ricci curvature are presented related to the stochastic heat equation.
Stichworte
stochastic heat equation; Ricci curvature; functional inequality; quasi-regular Dirichlet form
Erscheinungsjahr
2020
Zeitschriftentitel
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
Band
52
Ausgabe
3
Seite(n)
2237-2274
ISSN
0036-1410
eISSN
1095-7154
Page URI
https://pub.uni-bielefeld.de/record/2945134

Zitieren

Röckner M, Wu B, Zhu R, Zhu X. STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS. SIAM JOURNAL ON MATHEMATICAL ANALYSIS. 2020;52(3):2237-2274.
Röckner, M., Wu, B., Zhu, R., & Zhu, X. (2020). STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 52(3), 2237-2274. doi:10.1137/18M1211076
Röckner, M., Wu, B., Zhu, R., and Zhu, X. (2020). STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS. SIAM JOURNAL ON MATHEMATICAL ANALYSIS 52, 2237-2274.
Röckner, M., et al., 2020. STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 52(3), p 2237-2274.
M. Röckner, et al., “STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS”, SIAM JOURNAL ON MATHEMATICAL ANALYSIS, vol. 52, 2020, pp. 2237-2274.
Röckner, M., Wu, B., Zhu, R., Zhu, X.: STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS. SIAM JOURNAL ON MATHEMATICAL ANALYSIS. 52, 2237-2274 (2020).
Röckner, Michael, Wu, Bo, Zhu, Rongchan, and Zhu, Xiangchan. “STOCHASTIC HEAT EQUATIONS WITH VALUES IN A MANIFOLD VIA DIRICHLET FORMS”. SIAM JOURNAL ON MATHEMATICAL ANALYSIS 52.3 (2020): 2237-2274.

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