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...

in this paper vibration of ferromagnetic rectangular plates which are subjected to an inclined magnetic field is investigated based on classical plate theory and maxwell equations. levy type solution and finite element method using comsol software are used to obtain the frequency of the plate subjected to different boundary conditions, good agreements is obtained when computed results are compa...

Along an individual lifetime, stem cells replicate and suffer modifications in their DNA content. I model the modifications in the DNA of a single cell as a Levy flight, made up of small amplitude Brownian motions plus rare large-jumps events. The distribution function of mutations has a long tail, in which cancer events are located far away. The probability of cancer in a given tissue is rough...

This paper revisits Levy sections theorem, which generalizes the central limit theorem to encompass autocorrelated variables. Levy sections theorem’s approach is extended to time series and applied to historical daily returns of selected dollar exchange rates. We explain the elevated kurtosis usually observed in such series by their volatilities. In particular, the high kurtosis of emerging mar...