The chemical birth-death process with Gillespie noise

Abstract

A nontrivial technical issue has long plagued the literature on stochastic path integrals: it is not clear which definition is correct in the case of multiplicative/state-dependent noise. One reason for this is the unavailability of exactly solvable toy problems with state-dependent noise, that could in principle be used to compare the correctness of different approaches. In this paper, we provide an exact path integral calculation of the transition probability corresponding to a one-dimensional system with state-dependent noise. In particular, we solve the chemical birth-death process with Gillespie noise (the canonical continuous approximation to the discrete birth-death process often used as a toy model in chemical kinetics) using a Martin-Siggia-Rose-Janssen-De Dominicis (MSRJD) path integral. We verify that our result is correct by solving the Fokker-Planck equation via eigenfunction expansion.

20 pages

References in corpus (8)

• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Jarzynski Relation, Fluctuation Theorems, and Stochastic Thermodynamics for Non-Markovian Processes
• Towards Classification of Phase Transitions in Reaction--Diffusion Models
• Properties of Nonequilibrium Steady States: a Path Integral Approach
• On a new application of the path integrals in polymer statistical physics
• Stochastic path integrals can be derived like quantum mechanical path integrals
• Stochasticity or Noise in Biochemical Reactions
• The chemical birth-death process with additive noise