Some fractal properties of a class of self-similar Markov processes

AbstractFor a spectrally negative self-similar Markov process on $[0,\infty)$ with an a.s. finite overall supremum, we provide, in tractable detail, a kind of conditional Wiener–Hopf factorization at the maximum of the absorption time at zero, the conditioning being on the overall supremum and the jump at the overall supremum. In a companion result the Laplace transform of this absorption time (on the event that the process does not go above a given level) is identified under no other assumptions (such as the process admitting a recurrent extension and/or hitting zero continuously), generalizing some existing results in the literature.

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Intermittency and related issues in 16O-Ag/Br collision at 200A GeV/c

Canadian Journal of Physics ◽

10.1139/p10-038 ◽

2010 ◽

Vol 88 (8) ◽

pp. 575-584 ◽

Cited By ~ 4

Author(s):

M. K. Ghosh ◽

P. K. Haldar ◽

S. K. Manna ◽

A. Mukhopadhyay ◽

G. Singh

Keyword(s):

Particle Density ◽

Simulated Data ◽

Space Distribution ◽

Monte Carlo Code ◽

Final State ◽

Data Set ◽

Fractal Properties ◽

Self Similar ◽

Singly Charged ◽

Almost All

In this paper we present some results on the nonstatistical fluctuation in the 1-dimensional (1-d) density distribution of singly charged produced particles in the framework of the intermittency phenomenon. A set of nuclear emulsion data on 16O-Ag/Br interactions at an incident momentum of 200A GeV/c, was analyzed in terms of different statistical methods that are related to the self-similar fractal properties of the particle density function. A comparison of the present experiment with a similar experiment induced by the 32S nuclei and also with a set of results simulated by the Lund Monte Carlo code FRITIOF is presented. A similar comparison between this experiment and a pseudo-random number generated simulated data set is also made. The analysis reveals the presence of a weak intermittency in the 1-d phase space distribution of the produced particles. The results also indicate the occurrence of a nonthermal phase transition during emission of final-state hadrons. Our results on factorial correlators suggests that short-range correlations are present in the angular distribution of charged hadrons, whereas those on oscillatory moments show that such correlations are not restricted only to a few particles. In almost all cases, the simulated results fail to replicate their experimental counterparts.

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Continuous-State Branching Processes and Self-Similarity

Journal of Applied Probability ◽

10.1017/s0021900200005039 ◽

2008 ◽

Vol 45 (04) ◽

pp. 1140-1160 ◽

Cited By ~ 7

Author(s):

A. E. Kyprianou ◽

J. C. Pardo

Keyword(s):

Markov Processes ◽

Branching Processes ◽

Self Similarity ◽

Lamperti Transformation ◽

Continuous State ◽

Self Similar

In this paper we study the α-stable continuous-state branching processes (for α ∈ (1, 2]) and the α-stable continuous-state branching processes conditioned never to become extinct in the light of positive self-similarity. Understanding the interaction of the Lamperti transformation for continuous-state branching processes and the Lamperti transformation for positive, self-similar Markov processes gives access to a number of explicit results concerning the paths of α-stable continuous-state branching processes and α-stable continuous-state branching processes conditioned never to become extinct.

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