On the dual representations of Laplace transforms of Markov processes

2023/09/14 by Alexey N. Kuznetsov∥, Kuznetsov, Alexey, Yizao Wang +1
Business, Management and Accounting · Decision Sciences · #Advanced Queuing Theory Analysis #FOS: Mathematics #Probability (math.PR) #Simulation Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2309.08024

openalex publication_date 2023/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a general framework for dual representations of Laplace transforms of Markov processes. Such representations state that the Laplace transform of a finite-dimensional distribution of a Markov process can be expressed in terms of a Laplace transform involving another Markov process, but with coefficients in the Laplace transform and time indices of the process interchanged. Dual representations of Laplace transforms have been used recently to study open ASEP and to describe stationary measures of the open KPZ equation. Our framework covers both recently discovered examples in the literature and several new ones, involving general Lévy processes and certain birth-and-death processes.

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