Stochastic differential equations: loss of the Markov property by multiplicative noise

Dietrich Ryter

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arXiv · 1606.07464

Stochastic differential equations: loss of the Markov property by multiplicative noise

Dietrich Ryter

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Abstract

The solutions of SDEs with multiplicative noise are not Markovian. On a coarse-grained time scale they still are, but only in the "anti-Ito" case. This allows a simple computation of the most likely path. Any density peak moves along such a path, and its shape evolves according to further analytical formulas. This even provides some new insights into the asymptotic densities for large times, e.g. the criterion for attaining a quiescent steady state.

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Dietrich Ryter. 2016-06-20. Stochastic differential equations: loss of the Markov property by multiplicative noise. https://arxiv.org/abs/1606.07464

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