The chemical birth-death process with additive noise
arXiv:1910.09117
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.
arXiv comment24 pages
References in corpus (9)
- The Entropy Production of Ornstein-Uhlenbeck Active Particles: a path integral method for correlations
- Transition probabilities for general birth-death processes with applications in ecology, genetics, and evolution
- First Exit Times of Harmonically Trapped Particles: A Didactic Review
- Staggered Ladder Spectra
- The chemical Langevin equation: a path integral view of Gillespie's derivation
- 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
- On the transition of Charlier polynomials to the Hermite function
Cited by in corpus (3)
- 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
- Solving the chemical master equation for monomolecular reaction systems analytically: a Doi-Peliti path integral view