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