Special Issue "Stochastic Processes: Theory and Applications"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 July 2019

Special Issue Editors

Guest Editor
Prof. Dr. Alexander Zeifman

1. Department of Applied Mathematics, Vologda State University, Russia
2. Institute of Informatics Problems of the Federal Research Center ``Informatics and Control'', Russian Academy of Sciences, Russia
3. Vologda Research Center, Russian Academy of Sciences, Russia
Website | E-Mail
Interests: stochastic models; continuous-time Markov chains; queueing models; biological models
Guest Editor
Prof. Dr. Victor Korolev

1. Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Russia
2. Institute of Informatics Problems of the Federal Research Center “Informatics and Control”, Russian Academy of Sciences, Russia
3. Hangzhou Dianzi University, Hangzhou, China
Website | E-Mail
Interests: stochastic models; risk processes; queueing theory
Guest Editor
Prof. Dr. Alexander Sipin

Department of Applied Mathematics, Vologda State University, Russia
E-Mail
Interests: stochastic models; monte carlo methods

Special Issue Information

Dear Colleagues,

The aim of this Special Issue is to publish original research articles that cover recent advances in the theory and applications of stochastic processes. The focus will especially be on applications of stochastic processes as models of dynamic phenomena in various research areas, such as queuing theory, physics, biology, economics, medicine, reliability theory, and financial mathematics.

Potential topics include, but are not limited to:

  • Markov chains and processes
  • Large deviations and limit theorems
  • Random motions
  • Stochastic biological models
  • Reliability, availability, maintenance, inspection
  • Queueing models
  • Queueing network models
  • Computational methods for stochastic models
  • Applications to risk theory, insurance and mathematical finance

Prof. Dr. Alexander Zeifman
Prof. Dr. Victor Korolev
Prof. Dr. Alexander Sipin
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 850 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (3 papers)

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Research

Open AccessArticle
Estimating the Expected Discounted Penalty Function in a Compound Poisson Insurance Risk Model with Mixed Premium Income
Mathematics 2019, 7(3), 305; https://doi.org/10.3390/math7030305
Received: 24 February 2019 / Revised: 15 March 2019 / Accepted: 18 March 2019 / Published: 26 March 2019
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Abstract
In this paper, we consider an insurance risk model with mixed premium income, in which both constant premium income and stochastic premium income are considered. We assume that the stochastic premium income process follows a compound Poisson process and the premium sizes are [...] Read more.
In this paper, we consider an insurance risk model with mixed premium income, in which both constant premium income and stochastic premium income are considered. We assume that the stochastic premium income process follows a compound Poisson process and the premium sizes are exponentially distributed. A new method for estimating the expected discounted penalty function by Fourier-cosine series expansion is proposed. We show that the estimation is easily computed, and it has a fast convergence rate. Some numerical examples are also provided to show the good properties of the estimation when the sample size is finite. Full article
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
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Open AccessArticle
Monte Carlo Algorithms for the Parabolic Cauchy Problem
Mathematics 2019, 7(2), 177; https://doi.org/10.3390/math7020177
Received: 19 December 2018 / Revised: 30 January 2019 / Accepted: 12 February 2019 / Published: 15 February 2019
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Abstract
New Monte Carlo algorithms for solving the Cauchy problem for the second order parabolic equation with smooth coefficients are considered. Unbiased estimators for the solutions of this problem are constructed. Full article
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
Open AccessArticle
Cumulative Measure of Inaccuracy and Mutual Information in k-th Lower Record Values
Mathematics 2019, 7(2), 175; https://doi.org/10.3390/math7020175
Received: 17 December 2018 / Revised: 31 January 2019 / Accepted: 5 February 2019 / Published: 14 February 2019
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Abstract
In this paper, we discuss the cumulative measure of inaccuracy in k-lower record values and study characterization results of dynamic cumulative inaccuracy. We also present some properties of the proposed measures, and the empirical cumulative measure of inaccuracy in k-lower record [...] Read more.
In this paper, we discuss the cumulative measure of inaccuracy in k-lower record values and study characterization results of dynamic cumulative inaccuracy. We also present some properties of the proposed measures, and the empirical cumulative measure of inaccuracy in k-lower record values. We prove a central limit theorem for the empirical cumulative measure of inaccuracy under exponentially distributed populations. Finally, we analyze the mutual information for measuring the degree of dependency between lower record values, and we show that it is distribution-free. Full article
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
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