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Random walk approximation of BSDEs with Hölder continuous terminal condition. (English) Zbl 1433.60033

Summary: In this paper, we consider the random walk approximation of the solution of a Markovian BSDE whose terminal condition is a locally Hölder continuous function of the Brownian motion. We state the rate of the \(L_2\)-convergence of the approximated solution to the true one. The proof relies in part on growth and smoothness properties of the solution \(u\) of the associated PDE. Here we improve existing results by showing some properties of the second derivative of \(u\) in space.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
65C30 Numerical solutions to stochastic differential and integral equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
65C05 Monte Carlo methods

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