1
|
On the finiteness and tails of perpetuities under a Lamperti–Kiu MAP. J Appl Probab 2021. [DOI: 10.1017/jpr.2021.24] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
AbstractConsider a Lamperti–Kiu Markov additive process $(J, \xi)$ on $\{+, -\}\times\mathbb R\cup \{-\infty\}$, where J is the modulating Markov chain component. First we study the finiteness of the exponential functional and then consider its moments and tail asymptotics under Cramér’s condition. In the strong subexponential case we determine the subexponential tails of the exponential functional under some further assumptions.
Collapse
|
2
|
Véchambre G. General Self-Similarity Properties for Markov Processes and Exponential Functionals of Lévy Processes. J THEOR PROBAB 2021. [DOI: 10.1007/s10959-021-01097-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
|
3
|
Döring L, Weissmann P. Stable processes conditioned to hit an interval continuously from the outside. BERNOULLI 2020. [DOI: 10.3150/19-bej1134] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
4
|
Georgiou N, Mijatović A, Wade AR. Invariance principle for non-homogeneous random walks. ELECTRON J PROBAB 2019. [DOI: 10.1214/19-ejp302] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|
5
|
Sun X, Xiao Y, Xu L, Zhai J. Uniform dimension results for a family of Markov processes. BERNOULLI 2018. [DOI: 10.3150/17-bej994] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
|