Some explicit identities associated with positive self-similar Markov processes

被引:22
作者
Chaumont, L. [2 ]
Kyprianou, A. E. [3 ]
Pardo, J. C. [1 ,3 ]
机构
[1] Univ Paris 06, Lab Probabil & Modeles Aleatoires, 4 Pl Jussieu, F-75252 Paris 05, France
[2] Univ Angers, LAREMA, Dept Math, F-49045 Angers 01, France
[3] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England
基金
英国工程与自然科学研究理事会;
关键词
Positive self-similar Markov processes; Lamperti representation; Conditioned stable Levy processes; First exit time; First hitting time; Exponential functional; LEVY PROCESSES; FUNCTIONALS; OVERSHOOTS; ENTRANCE;
D O I
10.1016/j.spa.2008.05.001
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 consider some special classes of Levy processes with no gaussian component whose Levy measure is of the type pi(dx) = e(gamma x)nu(e(x) - 1) dx, where nu is the density of the stable Levy measure and gamma is a positive parameter which depends on its characteristics. These processes were introduced in [M. E. Caballero, L. Chaumont, Conditioned stable Levy processes and the Lamperti representation, J. Appl. Probab. 43 (2006) 967-983] as the underlying Levy processes in the Lamperti representation of conditioned stable Levy processes. In this paper, We Compute explicitly the law of these Levy processes at their first exit time from a finite or semi-finite interval, the law of their exponential functional and the first hitting time probability of a pair of points. (C) 2008 Elsevier B.V. All rights reserved.
引用
收藏
页码:980 / 1000
页数:21
相关论文
共 30 条
[11]  
Blumenthal R.M., 1961, Transactions of the American Mathematical Society, V99, P540, DOI [10.2307/1993561, DOI 10.2307/1993561]
[12]  
BOYARCHENKO S, 2002, NONGAUSSIAN MERTONBL
[13]   Conditioned stable Levy processes and the Lamperti representation [J].
Caballero, M. E. ;
Chaumont, L. .
JOURNAL OF APPLIED PROBABILITY, 2006, 43 (04) :967-983
[14]   Weak convergence of positive self-similar Markov processes and overshoots of levy processes [J].
Caballero, M. E. ;
Chaumont, L. .
ANNALS OF PROBABILITY, 2006, 34 (03) :1012-1034
[15]   The fine structure of asset returns: An empirical investigation [J].
Carr, P ;
Geman, H ;
Madan, DB ;
Yor, M .
JOURNAL OF BUSINESS, 2002, 75 (02) :305-332
[16]  
CHAUMONT L, STOCHASTIC PROCESS A, V64, P39
[17]   The lower envelope of positive self-similar Markov processes [J].
Chaumont, Loic ;
Pardo, J. C. .
ELECTRONIC JOURNAL OF PROBABILITY, 2006, 11 :1321-1341
[18]  
Cont R., 2004, Financ. Math. Ser., V65, P50
[19]   Overshoots and undershoots of Levy processes [J].
Doney, RA ;
Kyprianou, AE .
ANNALS OF APPLIED PROBABILITY, 2006, 16 (01) :91-106