Time Series Path Integral Expansions for Stochastic Processes

Abstract

A form of time series path integral expansion is provided that enables both analytic and numerical temporal effect calculations for a range of stochastic processes. Birth-death processes with linear rates are analysed via coherent state Doi-Peliti techniques. The $\mathfrak{su}(1,1)$ Lie algebra is utilised to capture quadratic rate birth-death processes. The techniques are also adapted to diffusion processes. All methods rely on finding a suitable reproducing kernel associated with the underlying algebra to perform the expansion. The resulting series differ from those found in standard Dyson time series field theory techniques.

21 Pages, 2 Figures

References in corpus (4)

• Dynamic first-order phase transition in kinetically constrained models of glasses
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Stochastic population dynamics in spatially extended predator-prey systems
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Cited by in corpus (1)

• Redundant basis interpretation of Doi-Peliti method and an application