Extended duality relations between birth-death processes and partial differential equations

Abstract

Duality relations between continuous-state and discrete-state stochastic processes with continuous-time have already been studied and used in various research fields. We propose extended duality relations, which enable us to derive discrete-state stochastic processes from arbitrary diffusion-type partial differential equations. The derivation is based on the Doi-Peliti formalism and the algebraic probability theory, and it will be clarified that additional states for the discrete-state stochastic processes must be considered in some cases.

13 pages

References in corpus (5)

• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Duality and hidden symmetries in interacting particle systems
• Duality for stochastic models of transport
• Algebraic probability, classical stochastic processes, and counting statistics
• On the notion(s) of duality for Markov processes

Cited by in corpus (15)

• Master equations and the theory of stochastic path integrals
• Squeezing stationary distributions of stochastic chemical reaction systems
• Duality relations between spatial birth-death processes and diffusions in Hilbert space
• Making Birth-Death Processes from Backward Fokker-Planck Equations for Computing Expectations in Langevin Systems
• Nonlinear Kalman filter based on duality relations between continuous and discrete-state stochastic processes
• Numerical methods to evaluate Koopman matrix from system equations
• Reaction Diffusion Systems and Extensions of Quantum Stochastic Processes
• Embedding stochastic differential equations into neural networks via dual processes
• Permutation of Tensor-Train Cores for Computing Moments on Stochastic Differential Equations
• Duality-based calculations for transition probabilities in stochastic chemical reactions
• Connection among stochastic Hamilton-Jacobi-Bellman equation, path-integral, and Koopman operator on nonlinear stochastic optimal control
• Redundant basis interpretation of Doi-Peliti method and an application
• Time Series Path Integral Expansions for Stochastic Processes
• Statistics for stochastic differential equations and approximations of resolvent
• Koopman operator-based discussion on partial observation in stochastic systems