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We present a probabilistic model of the microscopic scenario of dielectric relaxation. We prove a limit theorem for random sums of a special type that appear in the model. By means of the theorem, we show that the presented approach to relaxation phenomena leads to the well known Havriliak-Negami empirical dielectric response provided the physical quantities in the relaxation scheme have heavy-tailed distributions. The mathematical model, presented here in the context of dielectric relaxation, can...

Stochastic integral by a semi-Markov process of diffusion type.

Kharlamov, B.V. (2005)

Zapiski Nauchnykh Seminarov POMI

Stochastic model of accelerated testing methods of fatigue

Marie Šikulová (1974)

Aplikace matematiky

Stochastic reaction diffusion equations and interacting particle systems

G. Jona-Lasinio (1991)

Annales de l'I.H.P. Physique théorique

Stochastische Bewegungen und ihre ersten Integrale.

Hans Föllmer (1974/1975)

Jahresbericht der Deutschen Mathematiker-Vereinigung

Stoghastig behavior of an intermittently used system

Toshio Nakagawa, Amrit L. Goel, Shunji Osaki (1975)

RAIRO - Operations Research - Recherche Opérationnelle

Strict convexity of the limit shape in first-passage percolation.

Lalley, Steven P. (2003)

Electronic Communications in Probability [electronic only]

Strong hydrodynamic limit for attractive particle systems on $ℤ$ .

Bahadoran, Christophe, Guiol, Hervé, Ravishankar, Krishnamurthi, Saada, Ellen (2010)

Electronic Journal of Probability [electronic only]

Strong law of large numbers for the interface in ballistic deposition

Timo Seppäläinen (2000)

Annales de l'I.H.P. Probabilités et statistiques

Study of Queuing Systems with a Generalized Departure Process

Mirtchev, Seferin, Statev, Stanimir (2008)

Serdica Journal of Computing

This work was supported by the Bulgarian National Science Fund under grant BY-TH-105/2005.This paper deals with a full accessibility loss system and a single server delay system with a Poisson arrival process and state dependent exponentially distributed service time. We use the generalized service flow with nonlinear state dependence mean service time. The idea is based on the analytical continuation of the Binomial distribution and the classic M/M/n/0 and M/M/1/k system. We apply techniques based...