Path integral representation for stochastic jump processes with boundaries

Abstract

We propose a formalism to analyze discrete stochastic processes with finite-state-level N. By using an (N+1)-dimensional representation of su(2) Lie algebra, we re-express the master equation to a time-evolution equation for the state vector corresponding to the probability generating function. We found that the generating function of the system can be expressed as a propagator in the spin coherent state representation. The generating function has a path integral representation in terms of the spin coherent state. We apply our formalism to a linear Susceptible-Infected-Susceptible (SIS) epidemic model with time-dependent transition probabilities. The probability generating function of the system is calculated concisely using an algebraic property of the system or a path integral representation. Our results indicate that the method of analysis developed in the field of quantum mechanics is applicable to discrete stochastic processes with finite-state-level.

16 pages

References in corpus (5)

• Noise-Induced Bistable States and Their Mean Switching Time in Foraging Colonies
• Mapping out of equilibrium into equilibrium in one-dimensional transport models
• Noise-induced multistability in chemical systems: Discrete vs Continuum modeling
• Exact results for a noise-induced bistable system
• Theoretical Analysis of Discreteness-Induced Transition in Autocatalytic Reaction Dynamics