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. All methods rely on finding a suitable reproducing kernel associated with an underlying representative algebra to perform the expansion. Birth–death processes can be analysed with these techniques, using either standard Doi-Peliti coherent states, or the {mathfrak {s}}{mathfrak {u}}(1,1) Lie algebra. These result in simplest expansions for processes with linear or quadratic rates, respectively. The techniques are also adapted to diffusion processes. The resulting series differ from those found in standard Dyson time series field theory techniques.