### BSDE and generalized Dirichlet forms: The finite- dimensional case

Zhu R (2012)
Infinite Dimensional Analysis Quantum Probability And Related Topics 15(4): 1250022.

Zeitschriftenaufsatz | Veröffentlicht | Englisch

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Autor*in
Einrichtung
Abstract / Bemerkung
We consider the following quasi-linear parabolic system of backward partial differential equations (partial derivative(t) + L)u + f(., ., u, del u sigma) = 0 on [0, T] x R-d 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 Markov 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 of the PDE. A further main result is the generalization of the martingale representation theorem using the stochastic calculus associated to the generalized Dirichlet form given by L. The nonlinear term f satisfies a monotonicity condition with respect to u and a Lipschitz condition with respect to del(u).
Stichworte
forms; generalized Dirichlet; Dirichlet forms; partial differential equations; Backward stochastic differential equations; quasi-linear parabolic; Markov processes; martingale representation
Erscheinungsjahr
2012
Zeitschriftentitel
Infinite Dimensional Analysis Quantum Probability And Related Topics
Band
15
Ausgabe
4
Art.-Nr.
1250022
ISSN
0219-0257
Page URI
https://pub.uni-bielefeld.de/record/2578816

### Zitieren

Zhu R. BSDE and generalized Dirichlet forms: The finite- dimensional case. Infinite Dimensional Analysis Quantum Probability And Related Topics. 2012;15(4): 1250022.
Zhu, R. (2012). BSDE and generalized Dirichlet forms: The finite- dimensional case. Infinite Dimensional Analysis Quantum Probability And Related Topics, 15(4), 1250022. doi:10.1142/S0219025712500221
Zhu, R. (2012). BSDE and generalized Dirichlet forms: The finite- dimensional case. Infinite Dimensional Analysis Quantum Probability And Related Topics 15:1250022.
Zhu, R., 2012. BSDE and generalized Dirichlet forms: The finite- dimensional case. Infinite Dimensional Analysis Quantum Probability And Related Topics, 15(4): 1250022.
R. Zhu, “BSDE and generalized Dirichlet forms: The finite- dimensional case”, Infinite Dimensional Analysis Quantum Probability And Related Topics, vol. 15, 2012, : 1250022.
Zhu, R.: BSDE and generalized Dirichlet forms: The finite- dimensional case. Infinite Dimensional Analysis Quantum Probability And Related Topics. 15, : 1250022 (2012).
Zhu, Rongchan. “BSDE and generalized Dirichlet forms: The finite- dimensional case”. Infinite Dimensional Analysis Quantum Probability And Related Topics 15.4 (2012): 1250022.

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