Download or read book Limit Theorems for a One dimensional System with Random Switchings written by Tobias Hurth and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider a simple one-dimensional random dynamical system with two driving vector fields and random switchings between them. We show that this system satisfies a one force - one solution principle and compute its unique invariant density explicitly. We study the limiting behavior of the invariant density as the switching rate approaches zero and infinity and derive analogues of classical probabilistic results such as the central limit theorem and large deviations principle.
Download or read book Asymptotic Analyses for Complex Evolutionary Systems with Markov and Semi Markov Switching Using Approximation Schemes written by Yaroslav Chabanyuk and published by John Wiley & Sons. This book was released on 2020-10-02 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms written by Dmitri Koroliouk and published by John Wiley & Sons. This book was released on 2023-08-29 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates a number of asymptotic and analytic approaches applied for the study of random evolutionary systems, and considers typical problems for specific examples. In this case, constructive mathematical models of natural processes are used, which more realistically describe the trajectories of diffusion-type processes, rather than those of the Wiener process. We examine models where particles have some free distance between two consecutive collisions. At the same time, we investigate two cases: the Markov evolutionary system, where the time during which the particle moves towards some direction is distributed exponentially with intensity parameter λ; and the semi-Markov evolutionary system, with arbitrary distribution of the switching process. Thus, the models investigated here describe the motion of particles with a finite speed and the proposed random evolutionary process with characteristics of a natural physical process: free run and finite propagation speed. In the proposed models, the number of possible directions of evolution can be finite or infinite.
Download or read book Markov Random Flights written by Alexander D. Kolesnik and published by CRC Press. This book was released on 2021-01-04 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Markov Random Flights is the first systematic presentation of the theory of Markov random flights in the Euclidean spaces of different dimensions. Markov random flights is a stochastic dynamic system subject to the control of an external Poisson process and represented by the stochastic motion of a particle that moves at constant finite speed and changes its direction at random Poisson time instants. The initial (and each new) direction is taken at random according to some probability distribution on the unit sphere. Such stochastic motion is the basic model for describing many real finite-velocity transport phenomena arising in statistical physics, chemistry, biology, environmental science and financial markets. Markov random flights acts as an effective tool for modelling the slow and super-slow diffusion processes arising in various fields of science and technology. Features: Provides the first systematic presentation of the theory of Markov random flights in the Euclidean spaces of different dimensions. Suitable for graduate students and specialists and professionals in applied areas. Introduces a new unified approach based on the powerful methods of mathematical analysis, such as integral transforms, generalized, hypergeometric and special functions. Author Alexander D. Kolesnik is a professor, Head of Laboratory (2015–2019) and principal researcher (since 2020) at the Institute of Mathematics and Computer Science, Kishinev (Chișinău), Moldova. He graduated from Moldova State University in 1980 and earned his PhD from the Institute of Mathematics of the National Academy of Sciences of Ukraine, Kiev in 1991. He also earned a PhD Habilitation in mathematics and physics with specialization in stochastic processes, probability and statistics conferred by the Specialized Council at the Institute of Mathematics of the National Academy of Sciences of Ukraine and confirmed by the Supreme Attestation Commission of Ukraine in 2010. His research interests include: probability and statistics, stochastic processes, random evolutions, stochastic dynamic systems, random flights, diffusion processes, transport processes, random walks, stochastic processes in random environments, partial differential equations in stochastic models, statistical physics and wave processes. Dr. Kolesnik has published more than 70 scientific publications, mostly in high-standard international journals and a monograph. He has also acted as external referee for many outstanding international journals in mathematics and physics, being awarded by the "Certificate of Outstanding Contribution in Reviewing" from the journal "Stochastic Processes and their Applications." He was the visiting professor and scholarship holder at universities in Italy and Germany and member of the Board of Global Advisors of the International Federation of Nonlinear Analysts (IFNA), United States of America.
Download or read book Hybrid Switching Diffusions written by G. George Yin and published by Springer Science & Business Media. This book was released on 2009-10-03 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book encompasses the study of hybrid switching di usion processes and their applications. The word \hybrid" signi es the coexistence of c- tinuous dynamics and discrete events, which is one of the distinct features of the processes under consideration. Much of the book is concerned with the interactions of the continuous dynamics and the discrete events. Our motivations for studying such processes originate from emerging and - isting applications in wireless communications, signal processing, queueing networks, production planning, biological systems, ecosystems, nancial engineering, and modeling, analysis, and control and optimization of lar- scale systems, under the in uence of random environments. Displaying mixture distributions, switching di usions may be described by the associated operators or by systems of stochastic di erential eq- tions together with the probability transition laws of the switching actions. We either have Markov-modulated switching di usions or processes with continuous state-dependent switching. The latter turns out to be much more challenging to deal with. Viewing the hybrid di usions as a number of di usions joined together by the switching process, they may be se- ingly not much di erent from their di usion counterpart. Nevertheless, the underlying problems become more di cult to handle, especially when the switching processes depend on continuous states. The di culty is due to the interaction of the discrete and continuous processes and the tangled and hybrid information pattern.
Download or read book Asymptotic Behaviour of Linearly Transformed Sums of Random Variables written by V.V. Buldygin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Limit theorems for random sequences may conventionally be divided into two large parts, one of them dealing with convergence of distributions (weak limit theorems) and the other, with almost sure convergence, that is to say, with asymptotic prop erties of almost all sample paths of the sequences involved (strong limit theorems). Although either of these directions is closely related to another one, each of them has its own range of specific problems, as well as the own methodology for solving the underlying problems. This book is devoted to the second of the above mentioned lines, which means that we study asymptotic behaviour of almost all sample paths of linearly transformed sums of independent random variables, vectors, and elements taking values in topological vector spaces. In the classical works of P.Levy, A.Ya.Khintchine, A.N.Kolmogorov, P.Hartman, A.Wintner, W.Feller, Yu.V.Prokhorov, and M.Loeve, the theory of almost sure asymptotic behaviour of increasing scalar-normed sums of independent random vari ables was constructed. This theory not only provides conditions of the almost sure convergence of series of independent random variables, but also studies different ver sions of the strong law of large numbers and the law of the iterated logarithm. One should point out that, even in this traditional framework, there are still problems which remain open, while many definitive results have been obtained quite recently.
Download or read book Evolution of Systems in Random Media written by Vladimir S. Korolyuk and published by CRC Press. This book was released on 1995-09-11 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Evolution of Systems in Random Media is an innovative, application-oriented text that explores stochastic models of evolutionary stochastic systems in random media. Specially designed for researchers and practitioners who do not have a background in random evolutions, the book allows non-experts to explore the potential information and applications that random evolutions can provide.
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1995 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Central Limit Theorem for a One dimensional Polymer Measure written by Wolfgang König and published by . This book was released on 1994 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transactions of the American Mathematical Society written by and published by . This book was released on 1971 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random Motions in Markov and Semi Markov Random Environments 1 written by Anatoliy Pogorui and published by John Wiley & Sons. This book was released on 2021-03-16 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of two volumes on random motions in Markov and semi-Markov random environments. This first volume focuses on homogenous random motions. This volume consists of two parts, the first describing the basic concepts and methods that have been developed for random evolutions. These methods are the foundational tools used in both volumes, and this description includes many results in potential operators. Some techniques to find closed-form expressions in relevant applications are also presented. The second part deals with asymptotic results and presents a variety of applications, including random motion with different types of boundaries, the reliability of storage systems and solutions of partial differential equations with constant coefficients, using commutative algebra techniques. It also presents an alternative formulation to the Black-Scholes formula in finance, fading evolutions and telegraph processes, including jump telegraph processes and the estimation of the number of level crossings for telegraph processes.
Download or read book Markov Processes and Related Fields written by and published by . This book was released on 1995 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Random Motions in Markov and Semi Markov Random Environments 2 written by Anatoliy Pogorui and published by John Wiley & Sons. This book was released on 2021-03-16 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second of two volumes on random motions in Markov and semi-Markov random environments. This second volume focuses on high-dimensional random motions. This volume consists of two parts. The first expands many of the results found in Volume 1 to higher dimensions. It presents new results on the random motion of the realistic three-dimensional case, which has so far been barely mentioned in the literature, and deals with the interaction of particles in Markov and semi-Markov media, which has, in contrast, been a topic of intense study. The second part contains applications of Markov and semi-Markov motions in mathematical finance. It includes applications of telegraph processes in modeling stock price dynamics and investigates the pricing of variance, volatility, covariance and correlation swaps with Markov volatility and the same pricing swaps with semi-Markov volatilities.
Download or read book Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations written by Grigorij Kulinich and published by Springer Nature. This book was released on 2020-04-29 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to unstable solutions of stochastic differential equations (SDEs). Despite the huge interest in the theory of SDEs, this book is the first to present a systematic study of the instability and asymptotic behavior of the corresponding unstable stochastic systems. The limit theorems contained in the book are not merely of purely mathematical value; rather, they also have practical value. Instability or violations of stability are noted in many phenomena, and the authors attempt to apply mathematical and stochastic methods to deal with them. The main goals include exploration of Brownian motion in environments with anomalies and study of the motion of the Brownian particle in layered media. A fairly wide class of continuous Markov processes is obtained in the limit. It includes Markov processes with discontinuous transition densities, processes that are not solutions of any Itô's SDEs, and the Bessel diffusion process. The book is self-contained, with presentation of definitions and auxiliary results in an Appendix. It will be of value for specialists in stochastic analysis and SDEs, as well as for researchers in other fields who deal with unstable systems and practitioners who apply stochastic models to describe phenomena of instability.
Download or read book Government Reports Announcements written by and published by . This book was released on 1974 with total page 1000 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book U S Government Research Reports written by and published by . This book was released on 1963 with total page 964 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Selected Translations in Mathematical Statistics and Probability written by and published by American Mathematical Soc.. This book was released on 1985 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
