A Probabilistic Numerical Method for Fully Non-Linear Parabilic PDEs

Please enable javascript in your browser.

FAHIM, Arash | 2009

535 Viewed

Type of Document: Ph.D. Dissertation
Language: Farsi
Document No: 40212 (02)
University: Sharif University of Technology, Ecole Polytechnique
Department: Mathematical Sciences
Advisor(s): Touzi, Neyzar; Zohuri Zangeneh, Bijan
Abstract:
e solution for fully non-linear equations do not exists in general and for this reason the notion of viscosity solutions has been defined in this context. In this dissertation, a Monte carlo method is introduced for parabolic fully non-linear together with its asymptotics. In the proof of convergence, the method of [6] is used. en the rate of convergence from both sides is introduced: Finally, the error due to estimation of conditional expectation is derived for the estimation whose error is known with respect to sample size
Keywords:
Nonlinear Parabolic Equation ; Viscosity Solution ; Monotone Scheme ; Monte Carlo Approximation