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In this article we consider the Levy processes and the corresponding semi-group. We represent the generator of this semigroup in a convolution form. Using the obtained convolution form and the theory of integral equations we investigate the properties of a wide class of Levy processes (potential, quasi-potential, the probability of the Levy process remaining within the given domain, long time b...

We consider the problem of tracking visually identifiable mobile targets using a distributed system of mobile robots. We propose a behavior-based approach where mobile robots with limited sensory range use a search pattern observed in nature the Levy distributed search, to locate a mobile target. The Levy search pattern is inspired by the foraging pattern exhibited by social insects such as hon...

We propose a simple model based on the Gnedenko limit theorem for simulation and studies of the ordinary Levy motion, that is, a random process, whose increments are independent and distributed with a stable probability law. We use the generalized structure function for characterizing anomalous diffusion rate and propose to explore the modified Hurst method for empirical rescaled range analysis...