Intertwining Certain Fractional Derivatives

被引：23

作者：

Patie, Pierre ^{[1
]}

Simon, Thomas ^{[2
]}

机构：

[1] Univ Libre Bruxelles, Dept Math, B-1050 Brussels, Belgium

[2] Univ Lille 1, Lab Paul Painleve, F-59655 Villeneuve Dascq, France

来源：

POTENTIAL ANALYSIS | 2012年 / 36卷 / 04期

关键词：

Intertwining; Recurrent extension; Reflected process; Riemann-Liouville fractional derivative; Stable Levy process; LEVY PROCESSES; RECURRENT EXTENSIONS; ERGODICITY;

D O I：

10.1007/s11118-011-9241-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We obtain an intertwining relation between some Riemann-Liouville operators of order alpha aaEuro parts per thousand(1, 2), connecting through a certain multiplicative identity in law the one-dimensional marginals of reflected completely asymmetric alpha-stable L,vy processes. An alternative approach based on recurrent extensions of positive self-similar Markov processes and exponential functionals of L,vy processes is also discussed.

引用

页码：569 / 587

页数：19

共 28 条

[1] [Anonymous], 2006, THEORY APPL FRACTION
[2] [Anonymous], 1998, CONTINUOUS MARTINGAL
[3] Bernyk V., 2011, ANN PROBABI IN PRESS
[4] Bertoin J., 1996, Levy Processes
[5] Bertoin J, 1997, ANN APPL PROBAB, V7, P156
[6] Biane P., 1995, Semin. Probab. Strasbg, V29, P30
[7] BLUMENTHAL R. M., 1968, Markov Processes and Potential Theory
[8] Conditioned stable Levy processes and the Lamperti representation
Caballero, M. E.
Chaumont, L.
[J]. JOURNAL OF APPLIED PROBABILITY, 2006, 43 (04) : 967 - 983
[9] Carmona P, 1998, REV MAT IBEROAM, V14, P311
[10] Carmona P., 1994, STOCHAST REP, V47, P71

← 1 2 3 →