Nonstandard Martingales, Markov Chains and the Heat Equation
Probability
2017-04-20 v1
Abstract
We construct a nonstandard martingale from a discrete Markov chain. This is shown to be useful for solving the heat equation with a non smooth initial condition. We show that the nonstandard solution to the heat equation with a smooth initial condition specialises to the classical solution.
Keywords
Cite
@article{arxiv.1704.05530,
title = {Nonstandard Martingales, Markov Chains and the Heat Equation},
author = {Tristram de Piro},
journal= {arXiv preprint arXiv:1704.05530},
year = {2017}
}