this paper presents a class of theoretical and iterative method for linear partial differential equations. an algorithm and analytical solution with a initial condition is obtained using the reduced differential transform method. in this technique, the solution is calculated in the form of a series with easily computable components. there test modeling problems from mathematical mechanic, physi...

Ito’s construction of Markovian solutions to stochastic equations driven by a Lévy noise is extended to nonlinear distribution dependent integrands aiming at the effective construction of linear and nonlinear Markov semigroups and the corresponding processes with a given pseudo-differential generator. It is shown that a conditionally positive integro-differential operator (of the Lévy-Khintchin...

Degenerate parabolic equations of Kolmogorov type occur in many areas of analysis and applied mathematics. In their simplest form these equations were introduced by Kolmogorov in 1934 to describe the probability density of the positions and velocities of particles but the equations are also used as prototypes for evolution equations arising in the kinetic theory of gases. More recently equation...

This work (Part (I)) together with its companion (II)) develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear differential equations depending on the current as well past states. Because of complexity results, it seems to be instructive divide our contributions two parts. In contrast existing literature, effort is advance knowledge by allowing delay and dep...

Several researchers, including M. Gell-Mann, argue that the notion of Kolmogorov complexity, developed in the algorithmic information theory, is useful in physics (i.e., in the description of the physical world). Their arguments are rather convincing, but there seems to be a gap between traditional physical equations and Kolmogorov complexity: namely, it is not clear how the standard equations ...

The article proposes the concept of assessing level optimal load modes in terms tasks (flow tasks) for two groups students process integrated education specialty 126 "Information systems and technologies" 022 "Web design", by using toolkit Markov chains equations Kolmogorov. proposed approach allows you to reproduce dynamics states results mutual influence social groups, which are represented a...

We introduce the minimal maximally predictive models ( -machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and causal-state transitions are described by partial differential equations. Closed-form expressions are given for statistical complexities, excess entropies, and differential info...