arXiv subjects

Vladimir V. Uchaikin

Publications and source records attributed to Vladimir V. Uchaikin.

6 recordsLinked to original sources

arXiv2018

Parameter estimation for fractional Poisson processes

The paper proposes a formal estimation procedure for parameters of the fractional Poisson process (fPp). Such procedures are needed to make the fPp model usable in applied situations. The basic idea of fPp, motivated by experimental data with long memory is to make the standard Poisson model more flexible by permitting non-exponential, heavy-tailed distributions of interarrival times and different scaling properties. We establish the asymptotic normality of our estimators for the two parameters appearing in our fPp model. This fact permits construction of the corresponding confidence intervals. The properties of the estimators are then tested using simulated data.

stat.ME↗

arXiv2013

Transient processes in disordered semiconductor structures under dispersive transport conditions: Fractional calculus approach

We continue to develop a new approach to description of charge kinetics in disordered semiconductors. It is based on fractional diffusion equations. This article is devoted to transient processes in structures under dispersive transport conditions. We demonstrate that this approach allows us (i) to take into account energetic and topological types of disorder in common, (ii) to consider transport in samples with spatial distributions of localized states, and (iii) to describe transport in non-homogeneous materials with distributed dispersion parameter. Using fractional approach provides some specifications in interpretation of time-of-flight experiments in disordered semiconductors.

cond-mat.dis-nn↗

arXiv2011

Cosmic ray propagators in the fractional differential model of bounded anomalous diffusion

Fractional differential approach to cosmic ray physics problems is discussed. A short review in this field is given, some results are represented, analyzed and criticized. A new model called the bounded anomalous diffusion model is offered. Its equation includes the fractional material derivative which allows to take into account the finite speed of cosmic rays particles.

astro-ph.GA↗

arXiv2010

Fractional Boltzmann equation for resonance radiation transport in plasma

The fractional Boltzmann equation for resonance radiation transport in plasma is proposed. We start from the standard Boltzmann equation, averaging over frequencies leads to appearance of fractional derivative. This fact is in accordance with the conception of latent variables leading to hereditary and non-local dynamics (in particular, fractional dynamics). The presence of the fractional material derivative in the equation is concordant with heavy tailed distribution of photon path lengths and with spatiotemporal coupling peculiar to the process. We discuss some methods of solution of the obtained equation and demonstrate numerical results in some simple cases.

physics.plasm-ph↗

arXiv2010

Truncated Levy statistics for transport in disordered semiconductors

Probabilistic interpretation of transition from the dispersive transport regime to the quasi-Gaussian one in disordered semiconductors is given in terms of truncated Levy distributions. Corresponding transport equations with fractional order derivatives are derived. We discuss physical causes leading to truncated waiting time distributions in the process and describe influence of truncation on carrier packet form, transient current curves and frequency dependence of conductivity. Theoretical results are in a good agreement with experimental facts.

cond-mat.dis-nn↗

arXiv2010

Fractional processes: from Poisson to branching one

Fractional generalizations of the Poisson process and branching Furry process are considered. The link between characteristics of the processes, fractional differential equations and Levy stable densities are discussed and used for construction of the Monte Carlo algorithm for simulation of random waiting times in fractional processes. Numerical calculations are performed and limit distributions of the normalized variable Z=N/ are found for both processes.

cond-mat.stat-mech↗