期刊名称：Latin American Journal of Probability and Mathematical Statistics
电子版ISSN：1980-0436
出版年度：2018
卷号：XV
期号：2
页码：1257-1292
DOI：10.30757/ALEA.v15-47
出版社：Instituto Nacional De Matemática Pura E Aplicada
摘要：Markov Additive Processes are bi-variate Markov processes of the form(ξ, J) =(ξt, Jt), t > 0which should be thought of as a multi-type L´evy process:the second component J is a Markov chain on a finite space {1, . . . ,K}, and thefirst component ξ behaves locally as a L´evy process with dynamics depending on J.In the subordinator-like case where ξ is nondecreasing, we establish several resultsconcerning the moments of ξ and of its exponential functional Iξ =R ∞0 e−ξtdt,extending the work of Carmona et al. (1997), and Bertoin and Yor (2001).We then apply these results to the study of multi-type self-similar fragmentationprocesses: these are self-similar transformations of Bertoin’s homogeneous multitypefragmentation processes, introduced in Bertoin (2008). Notably, we encode thegenealogy of the process in an R-tree as in Haas and Miermont (2004), and undersome Malthusian hypotheses, compute its Hausdorff dimension in a generalisationof our previous results in Stephenson (2013).
