scholarly journals Construction and asymptotic behavior of a class of self-similar stable processes

1996 ◽  
Vol 22 (2) ◽  
pp. 275-283
Author(s):  
Toshio MORI ◽  
Yumiko SATO
Keyword(s):  
Asymptotic Behavior ◽  
Stable Processes ◽  
Self Similar

scholarly journals Self-Similar Blow-Up Solutions of the KPZ Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-4 ◽  
Author(s):  
Alexander Gladkov
Keyword(s):  
Asymptotic Behavior ◽  
Blow Up ◽  
Kpz Equation ◽  
Self Similar ◽  
The Kpz Equation ◽  
Similar Solutions

Self-similar blow-up solutions for the generalized deterministic KPZ equationut=uxx+|ux|qwithq>2are considered. The asymptotic behavior of self-similar solutions is studied.

Universal self-similar asymptotic behavior of optical bump spreading in random medium atop incoherent background: reply

2020 ◽  
Vol 45 (13) ◽  
pp. 3511
Author(s):  
Xiaofei Li ◽  
Sergey A. Ponomarenko ◽  
Zhiheng Xu ◽  
Fei Wang ◽  
Yangjian Cai ◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Random Medium ◽  
Self Similar

Integral equation for the causal distributions and their self-similar asymptotic behavior in the ladder ?3 model

1980 ◽  
Vol 45 (3) ◽  
pp. 1041-1048
Author(s):  
A. N. Kvinikhidze ◽  
B. A. Magradze ◽  
V. A. Matveev ◽  
M. A. Mestvirishvili ◽  
A. N. Tavkhelidze
Keyword(s):  
Integral Equation ◽  
Asymptotic Behavior ◽  
Self Similar

scholarly journals From infinite urn schemes to self-similar stable processes

2020 ◽  
Vol 130 (4) ◽  
pp. 2471-2487 ◽  
Author(s):  
Olivier Durieu ◽  
Gennady Samorodnitsky ◽  
Yizao Wang
Keyword(s):  
Stable Processes ◽  
Self Similar

scholarly journals Deep Factorisation of the Stable Process III: the View from Radial Excursion Theory and the Point of Closest Reach

2019 ◽  
Vol 53 (4) ◽  
pp. 1347-1375
Author(s):  
Andreas E. Kyprianou ◽  
Victor Rivero ◽  
Weerapat Satitkanitkul
Keyword(s):  
Stationary Distribution ◽  
Markov Processes ◽  
Stable Process ◽  
Stable Processes ◽  
Excursion Theory ◽  
Self Similar ◽  
Isotropic Stable Process

AbstractWe compute explicitly the distribution of the point of closest reach to the origin in the path of any d-dimensional isotropic stable process, with d ≥ 2. Moreover, we develop a new radial excursion theory, from which we push the classical Blumenthal–Getoor–Ray identities for first entry/exit into a ball (cf. Blumenthal et al. Trans. Amer. Math. Soc., 99, 540–554 1961) into the more complex setting of n-tuple laws for overshoots and undershoots. We identify explicitly the stationary distribution of any d-dimensional isotropic stable process when reflected in its running radial supremum. Finally, for such processes, and as consequence of some of the analysis of the aforesaid, we provide a representation of the Wiener–Hopf factorisation of the MAP that underlies the stable process through the Lamperti–Kiu transform. Our analysis continues in the spirit of Kyprianou (Ann. Appl. Probab., 20(2), 522–564 2010) and Kyprianou et al. (2015) in that our methodology is largely based around treating stable processes as self-similar Markov processes and, accordingly, taking advantage of their Lamperti-Kiu decomposition.

Sign in / Sign up

Export Citation Format

Share Document