BSDE and generalized Dirichlet forms: The infinite dimensional case

Zhu R (2015)
Forum Mathematicum 27(1): 201-253.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
Download
Es wurden keine Dateien hochgeladen. Nur Publikationsnachweis!
Abstract / Bemerkung
We consider the following quasi-linear parabolic system of backward partial differential equations on a Banach space E: (partial derivative t + L)u + f(., ., u, A(1/2)del u) = 0 on [0, T] x E, u(T) = phi, where L is a possibly degenerate second-order differential operator with merely measurable coefficients. We solve this system in the framework of generalized Dirichlet forms and employ the stochastic calculus associated to the Markoy process with generator L to obtain a probabilistic representation of the solution u by solving the corresponding backward stochastic differential equation. The solution satisfies the corresponding mild equation which is equivalent to being a generalized solution to the PDE. A further main result is the generalization of the martingale representation theorem in infinite dimension using the stochastic calculus associated to the generalized Dirichlet form given by L. The tic -linear term f satisfies a monotonicity condition with respect to u and a Lipschitz condition with respect to del u.
Stichworte
forms; Markov processes martingale representation. Kolmogorov equations.; generalized Dirichlet; Dirichlet forms; partial differential equations; quasi-linear parabolic; Backward stochastic differential equations
Erscheinungsjahr
2015
Zeitschriftentitel
Forum Mathematicum
Band
27
Ausgabe
1
Seite(n)
201-253
ISSN
0933-7741
Page URI
https://pub.uni-bielefeld.de/record/2720306

Zitieren

Zhu R. BSDE and generalized Dirichlet forms: The infinite dimensional case. Forum Mathematicum. 2015;27(1):201-253.
Zhu, R. (2015). BSDE and generalized Dirichlet forms: The infinite dimensional case. Forum Mathematicum, 27(1), 201-253. doi:10.1515/forum-2012-0007
Zhu, R. (2015). BSDE and generalized Dirichlet forms: The infinite dimensional case. Forum Mathematicum 27, 201-253.
Zhu, R., 2015. BSDE and generalized Dirichlet forms: The infinite dimensional case. Forum Mathematicum, 27(1), p 201-253.
R. Zhu, “BSDE and generalized Dirichlet forms: The infinite dimensional case”, Forum Mathematicum, vol. 27, 2015, pp. 201-253.
Zhu, R.: BSDE and generalized Dirichlet forms: The infinite dimensional case. Forum Mathematicum. 27, 201-253 (2015).
Zhu, Rongchan. “BSDE and generalized Dirichlet forms: The infinite dimensional case”. Forum Mathematicum 27.1 (2015): 201-253.

Export

Markieren/ Markierung löschen
Markierte Publikationen

Open Data PUB

Web of Science

Dieser Datensatz im Web of Science®

Suchen in

Google Scholar