Nonstandard Martingales, Markov Chains and the Heat Equation

2017/04/15 by Tristram de Piro, de Piro, Tristram
Mathematics · Physics and Astronomy · #FOS: Mathematics #Mathematical and Theoretical Analysis #Probability (math.PR) #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.1704.05530

openalex publication_date 2017/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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