G-expectations in infinite dimensional spaces and related PDEs
Probability
2013-06-25 v1
Abstract
In this paper, we extend the G-expectation theory to infinite dimensions. Such notions as a covariation set of G-normal distributed random variables, viscosity solution, a stochastic integral driven by G-Brownian motion are introduced and described in the given infinite dimensional case. We also give a probabilistic representation of the unique viscosity solution to the fully nonlinear parabolic PDE with unbounded first order term in Hilbert space in terms of G-expectation theory.
Keywords
Cite
@article{arxiv.1306.5272,
title = {G-expectations in infinite dimensional spaces and related PDEs},
author = {Anton Ibragimov},
journal= {arXiv preprint arXiv:1306.5272},
year = {2013}
}
Comments
The paper is based on the author's Ph.D. thesis