Stochastic extrema as stationary phases of characteristic functions

TL;DR

This paper explores the semi-classical asymptotics of a stochastic process's characteristic function using stationary phase methods, defining stochastic extrema via the complex logarithm's limit values and proposing a numerical calculation approach.

Contribution

It introduces a novel connection between stochastic extrema and stationary phases of characteristic functions, along with a numerical method for their computation.

Findings

Characterization of stochastic extrema through complex logarithm limits

Application of stationary phase method to stochastic process analysis

Development of a numerical approach for calculating stochastic extrema

Abstract

The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The extremal range for a stochastic process is defined by limit values of the complex logarithm of the characteristic function. The paper also outlines a numerical method for calculating stochastic extrema.