6533b858fe1ef96bd12b62f5

RESEARCH PRODUCT

Random walk approximation of BSDEs with H{\"o}lder continuous terminal condition

Céline LabartChristel GeissAntti Luoto

subject

Statistics and Probabilitynumerical schemeHölder conditionSpace (mathematics)01 natural sciences010104 statistics & probabilityMathematics::Probability0101 mathematicsBrownian motionrandom walk approximationSecond derivativeMathematicsstokastiset prosessitSmoothness (probability theory)numeeriset menetelmät010102 general mathematicsMathematical analysisSpeed of convergenceBackward stochastic differential equationsFunction (mathematics)State (functional analysis)Random walk[MATH.MATH-PR]Mathematics [math]/Probability [math.PR]random walk approxi-mationbackward stochastic differential equationsspeed of convergencespeed of convergence MSC codes : 65C30 60H35 60G50 65G99Mathematics - Probability

description

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 L2-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. peerReviewed

yearjournalcountryeditionlanguage
2018-09-14
http://arxiv.org/abs/1806.07674