Exponential functionals of Markov additive processes

被引：6
|
作者：
Behme, Anita [1 ]
Sideris, Apostolos [1 ]
机构：
[1] Tech Univ Dresden, Dresden, Germany
来源：
ELECTRONIC JOURNAL OF PROBABILITY | 2020年 / 25卷
关键词：
exponential functional; Levy process; Markov additive process; Markov modulated perpetuity; Markov switching model; LEVY; FACTORIZATION; STATIONARITY; STABILITY;
D O I：
10.1214/20-EJP441
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We provide necessary and sufficient conditions for convergence of exponential integrals of Markov additive processes. By contrast with the classical Levy case studied by Erickson and Maller we have to distinguish between almost sure convergence and convergence in probability. Our proofs rely on recent results on perpetuities in a Markovian environment by Alsmeyer and Buckmann.
引用
收藏
页数：25
相关论文
共 50 条
  • [1] On moments of integral exponential functionals of additive processes
    Salminen, Paavo
    Vostrikova, Lioudmila
    STATISTICS & PROBABILITY LETTERS, 2019, 146 : 139 - 146
  • [2] On moments of integrals with respect to Markov additive processes and of Markov modulated generalized Ornstein-Uhlenbeck processes
    Behme, Anita
    Di Tella, Paolo
    Sideris, Apostolos
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2024, 174
  • [3] The entrance laws of self-similar Markov processes and exponential functionals of Levy processes
    Bertoin, J
    Yor, M
    POTENTIAL ANALYSIS, 2002, 17 (04) : 389 - 400
  • [4] Exponential Functionals of Levy Processes with Jumps
    Behme, Anita
    ALEA-LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS, 2015, 12 (01): : 375 - 397
  • [5] Exponential functionals of Levy processes
    Bertoin, Jean
    Yor, Marc
    PROBABILITY SURVEYS, 2005, 2 : 191 - 212
  • [6] ON EXPONENTIAL FUNCTIONALS OF PROCESSES WITH INDEPENDENT INCREMENTS
    Salminen, P.
    Vostrikova, L.
    THEORY OF PROBABILITY AND ITS APPLICATIONS, 2018, 63 (02) : 267 - 291
  • [7] On Exponential Functionals of L,vy Processes
    Behme, Anita
    Lindner, Alexander
    JOURNAL OF THEORETICAL PROBABILITY, 2015, 28 (02) : 681 - 720
  • [8] The Entrance Laws of Self-Similar Markov Processes and Exponential Functionals of Lévy Processes
    Jean Bertoin
    Marc Yor
    Potential Analysis, 2002, 17 : 389 - 400
  • [9] Distributional properties of exponential functionals of Levy processes
    Kuznetsov, A.
    Pardo, J. C.
    Savov, M.
    ELECTRONIC JOURNAL OF PROBABILITY, 2012, 17 : 1 - 35
  • [10] Asymptotic results for exponential functionals of Levy processes
    Li, Zenghu
    Xu, Wei
    STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2018, 128 (01) : 108 - 131
12345