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- W1710484893 abstract "Recently, ultraslow Gaussian converging stochastic process and the growth rate of value distribution problem have been studied by random walks of nonequilibrium systems in physics [l] and iterated function analysis of dynamical systems in mathematics [2]. The Levy walk is the one considered as stable non-Gaussian random process. The natural question to ask, is that are there any other non-Gaussian random processes interesting to us? We propose that Catalan random walk is playing the role. Levy walk is a random walk performed by visiting the same sites of Levy flight. Instantaneous jumps are responsible for the infinite variances which are not allowed, and a time sequence is introduced so that long steps are penalized. One possible resolution of the paradox of infinite variance is provided by Levy walks. Levy walks have infinite variance and can be differentiated, but this resolution applies only when a spatio-temporal coupling is present. The paradox of infinite variance may also be resolved by introducing a variance of the Levy flight which does not require the hypothesis of a spatio-temporal coupling. In physical systems, the variance of any stationary processes is finite, so that a Gaussian behavior is expected in the absence of long range correlation. Gaussian behavior arises from the central limit theorem (CLT) which is fundamental to statistical mechanics. It states that the sum" @default.
- W1710484893 created "2016-06-24" @default.
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- W1710484893 date "1996-12-01" @default.
- W1710484893 modified "2023-09-26" @default.
- W1710484893 title "Catalan Random Walks and Flights" @default.
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