The standard central limit theorem plays a fundamental role in Boltzmann-Gibbs statistical mechanics. This important physical theory has been generalized [1] in 1988 by using the entropy Sq = 1âˆ’ P iâ€¦ (More)

In this paper we construct new random walks connected with fractional order differential equations. Namely, the governing equations corresponding to the constructed random walks are multi-term orâ€¦ (More)

It is known that if a stochastic process is a solution to a classical ItÃ´ stochastic differential equation (SDE), then its transition probabilities satisfy in the weak sense the associated Cauchyâ€¦ (More)

The well known Duhamelâ€™s principle allows to reduce the Cauchy problem for a linear inhomogeneous partial differential equation to the Cauchy problem for the corresponding homogeneous equation. Inâ€¦ (More)

In this paper the multi-dimensional Monte-Carlo random walk simulation models governed by distributed fractional order differential equations (DODEs) and multi-term fractional order differentialâ€¦ (More)

nonextensive statistical mechanics is a one-parameter description of correlated states. In this paper we use a translated entropic index: 1-q q â†’. The essence of this translation is to improve theâ€¦ (More)

The classic central limit theorem and Î±-stable distributions play a key role in probability theory, and also in Boltzmann-Gibbs (BG) statistical mechanics. They both concern the paradigmatic case ofâ€¦ (More)