The chemical birth-death process with additive noise

John J. Vastola

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arXiv · 1910.09117

The chemical birth-death process with additive noise

John J. Vastola

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Abstract

The chemical birth-death process, whose chemical master equation (CME) is exactly solvable, is a paradigmatic toy problem often used to get intuition for how stochasticity affects chemical kinetics. In a certain limit, it can be approximated by an Ornstein-Uhlenbeck-like process which is also exactly solvable. In this paper, we use this system to showcase eight qualitatively different ways to exactly solve continuous stochastic systems: (i) integrating the stochastic differential equation; (ii) computing the characteristic function; (iii) eigenfunction expansion; (iv) using ladder operators; (v) the Martin-Siggia-Rose-Janssen-De Dominicis path integral; (vi) the Onsager-Machlup path integral; (vii) semiclassically approximating the Onsager-Machlup path integral; and (viii) approximating the solution to the corresponding CME.

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John J. Vastola. 2019-10-21. The chemical birth-death process with additive noise. https://arxiv.org/abs/1910.09117

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