Interfacial Phenomena and Natural Local Time

TL;DR

This paper introduces 'natural local time', a modified local time concept for stochastic processes, to better analyze phenomena involving interfaces with discontinuous dispersion coefficients in geophysical and biological sciences.

Contribution

It proposes a new form of local time tailored for processes with interfaces, linking micro-scale observations to macro-scale environmental parameters.

Findings

New formulation of local time for interface problems

Application to geophysical and biological dispersion phenomena

Enhanced inference of macro-scale parameters from micro-scale data

Abstract

This article addresses a modification of local time for stochastic processes, to be referred to as `natural local time'. It is prompted by theoretical developments arising in mathematical treatments of recent experiments and observations of phenomena in the geophysical and biological sciences pertaining to dispersion in the presence of an interface of discontinuity in dispersion coefficients. The results illustrate new ways in which to use the theory of stochastic processes to infer macro scale parameters and behavior from micro scale observations in particular heterogeneous environments.