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arXiv · 1704.05530

Nonstandard Martingales, Markov Chains and the Heat Equation

Tristram de Piro
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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.

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Tristram de Piro. 2017-04-15. Nonstandard Martingales, Markov Chains and the Heat Equation. https://arxiv.org/abs/1704.05530

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