Stability of overshoots of Markov additive processes Article Swipe
Related Concepts
Mathematics
Ergodic theory
Mixing (physics)
Markov chain
Stability (learning theory)
Markov process
Factorization
Transformation (genetics)
Pure mathematics
Space (punctuation)
Applied mathematics
Statistical physics
Statistics
Computer science
Algorithm
Machine learning
Gene
Operating system
Physics
Chemistry
Biochemistry
Quantum mechanics
Leif Döring
,
Lukas Trottner
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1214/23-aap1951
· OA: W3126880441
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.1214/23-aap1951
· OA: W3126880441
We prove precise stability results for overshoots of Markov additive\nprocesses (MAPs) with finite modulating space. Our approach is based on the\nMarkovian nature of overshoots of MAPs whose mixing and ergodic properties are\ninvestigated in terms of the characteristics of the MAP. On our way we extend\nfluctuation theory of MAPs, contributing among others to the understanding of\nthe Wiener-Hopf factorization for MAPs by generalizing Vigon's \\'equations\namicales invers\\'es known for L\\'evy processes. Using the Lamperti\ntransformation the results can be applied to self-similar Markov processes.\nAmong many possible applications, we study the mixing behavior of stable\nprocesses sampled at first hitting times as a concrete example.\n
Related Topics
Finding more related topics…