The chemical birth-death process with additive noise

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.

24 pages

References in corpus (3)

• Stochastic path integrals can be derived like quantum mechanical path integrals
• Stochasticity or Noise in Biochemical Reactions
• Approximation of the first passage time distribution for the birth-death processes

Cited by in corpus (2)

• Analytic solution of chemical master equations involving gene switching. I: Representation theory and diagrammatic approach to exact solution
• The chemical birth-death process with Gillespie noise