Numerical schemes for multivalued backward stochastic differential systems
- 71 Downloads
We define approximation schemes for generalized backward stochastic differential systems, considered in the Markovian framework. More precisely, we propose a mixed approximation scheme for the following backward stochastic variational inequality:
where ∂φ is the subdifferential operator of a convex lower semicontinuous function φ and (X t ) t∈[0;T] is the unique solution of a forward stochastic differential equation. We use an Euler type scheme for the system of decoupled forward-backward variational inequality in conjunction with Yosida approximation techniques.
$$dY_t + F(t,X_t ,Y_t ,Z_t )dt \in \partial \phi (Y_t )dt + Z_t dW_t ,$$
KeywordsEuler scheme Yosida approximation Error estimate Multivalued backward SDEs Reflected SDEs
MSC65C99 60H30 47H15
Unable to display preview. Download preview PDF.
- Karatzas I., Shreve S.E., Brownian Motion and Stochastic Calculus, Grad. Texts in Math., 113, Springer, New York, 1988Google Scholar
- Kloeden P.E., Platen E., Numerical Solution of Stochastic Differential Equations, Appl. Math. (N. Y.), Springer, Berlin, 1992Google Scholar
- Pardoux É., Peng S., Backward stochastic differential equations and quasilinear parabolic partial differential equations, In: Stochastic Partial Differential Equations and their Applications, Charlotte, June 6–8, 1991, Lecture Notes in Control and Inform. Sci., 176, Springer, Berlin, 1992, 200–217CrossRefGoogle Scholar
- SŁominski L., On approximation of solutions of multidimensional SDEs with reflecting boundary conditions, Stochastic Process. Appl., 1994, 50(2), 179–219Google Scholar
- Zhang J., Some Fine Properties of Backward Stochastic Differential Equations, PhD thesis, Purdue University, 2001Google Scholar
© © Versita Warsaw and Springer-Verlag Wien 2011