Concatenation and Pasting of Right Processes

TL;DR

This paper introduces a universal method for concatenating Markov right processes and demonstrates its application to constructing locally defined processes such as Brownian motions on compact intervals.

Contribution

It presents a novel universal approach for concatenating Markov right processes and applies it to pathwise constructions of local processes.

Findings

Established a universal concatenation method for Markov right processes

Applied the method to construct Brownian motions on compact intervals

Facilitated pathwise constructions of locally defined stochastic processes

Abstract

A universal method for the concatenation of a sequence of Markov right processes is established. It is then applied to the continued pasting of two Markov right processes, which can be used for pathwise constructions of locally defined processes like Brownian motions on compact intervals.