Inhomogeneous Random Evolutions and Their Applications PDF Download

Author: Anatoliy Swishchuk
Publisher: CRC Press
ISBN: 0429855052
Category : Mathematics
Languages : en
Pages : 253

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Book Description
Inhomogeneous Random Evolutions and Their Applications explains how to model various dynamical systems in finance and insurance with non-homogeneous in time characteristics. It includes modeling for: financial underlying and derivatives via Levy processes with time-dependent characteristics; limit order books in the algorithmic and HFT with counting price changes processes having time-dependent intensities; risk processes which count number of claims with time-dependent conditional intensities; multi-asset price impact from distressed selling; regime-switching Levy-driven diffusion-based price dynamics. Initial models for those systems are very complicated, which is why the author’s approach helps to simplified their study. The book uses a very general approach for modeling of those systems via abstract inhomogeneous random evolutions in Banach spaces. To simplify their investigation, it applies the first averaging principle (long-run stability property or law of large numbers [LLN]) to get deterministic function on the long run. To eliminate the rate of convergence in the LLN, it uses secondly the functional central limit theorem (FCLT) such that the associated cumulative process, centered around that deterministic function and suitably scaled in time, may be approximated by an orthogonal martingale measure, in general; and by standard Brownian motion, in particular, if the scale parameter increases. Thus, this approach allows the author to easily link, for example, microscopic activities with macroscopic ones in HFT, connecting the parameters driving the HFT with the daily volatilities. This method also helps to easily calculate ruin and ultimate ruin probabilities for the risk process. All results in the book are new and original, and can be easily implemented in practice.

Author: Anatoly Swishchuk
Publisher: Springer Science & Business Media
ISBN: 9401157545
Category : Mathematics
Languages : en
Pages : 212

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Book Description
The main purpose of this handbook is to summarize and to put in order the ideas, methods, results and literature on the theory of random evolutions and their applications to the evolutionary stochastic systems in random media, and also to present some new trends in the theory of random evolutions and their applications. In physical language, a random evolution ( RE ) is a model for a dynamical sys tem whose state of evolution is subject to random variations. Such systems arise in all branches of science. For example, random Hamiltonian and Schrodinger equations with random potential in quantum mechanics, Maxwell's equation with a random refractive index in electrodynamics, transport equations associated with the trajec tory of a particle whose speed and direction change at random, etc. There are the examples of a single abstract situation in which an evolving system changes its "mode of evolution" or "law of motion" because of random changes of the "environment" or in a "medium". So, in mathematical language, a RE is a solution of stochastic operator integral equations in a Banach space. The operator coefficients of such equations depend on random parameters. Of course, in such generality , our equation includes any homogeneous linear evolving system. Particular examples of such equations were studied in physical applications many years ago. A general mathematical theory of such equations has been developed since 1969, the Theory of Random Evolutions.

Author: Anatoliĭ Vitalʹevich Svishchuk
Publisher:
ISBN:
Category : Banach spaces
Languages : en
Pages : 0

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Book Description
"The book deals with inhomogeneous REs and their applications, which are more general and more applicable because they describe in a much better way the evolutions of many processes in real world, which have no homogeneous evolution/behaviour, including economics, finance and insurance"--Provided by publisher.

Author: Nikolaos Limnios
Publisher: Springer Nature
ISBN: 3031334299
Category : Mathematics
Languages : en
Pages : 206

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Book Description
This book extends the theory and applications of random evolutions to semi-Markov random media in discrete time, essentially focusing on semi-Markov chains as switching or driving processes. After giving the definitions of discrete-time semi-Markov chains and random evolutions, it presents the asymptotic theory in a functional setting, including weak convergence results in the series scheme, and their extensions in some additional directions, including reduced random media, controlled processes, and optimal stopping. Finally, applications of discrete-time semi-Markov random evolutions in epidemiology and financial mathematics are discussed. This book will be of interest to researchers and graduate students in applied mathematics and statistics, and other disciplines, including engineering, epidemiology, finance and economics, who are concerned with stochastic models of systems.

Author: Hocine Cherifi
Publisher: Cambridge Scholars Publishing
ISBN: 1443863246
Category : Mathematics
Languages : en
Pages : 355

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Book Description
Fuelled by the big data paradigm, the study of networks is an interdisciplinary field that is growing at the interface of many branches of science including mathematics, physics, computer science, biology, economics and the social sciences. This book, written by experts from the Network Science community, covers a wide range of theoretical and practical advances in this highly active field, highlighting the strong interconnections between works in different disciplines. The eleven chapters take the reader through the essential concepts for the structural analysis of networks, and their applications to real-world scenarios. Being self-contained, the book is intended for researchers, graduate and advanced undergraduate students from different intellectual backgrounds. Each chapter combines mathematical rigour with rich references to the literature, while remaining accessible to a wide range of readers who wish to understand some of the key issues encountered in many aspects of networked everyday life.

Author: Rosa Maria Benito
Publisher: Springer Nature
ISBN: 3030934098
Category : Technology & Engineering
Languages : en
Pages : 896

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Book Description
This book highlights cutting-edge research in the field of network science, offering scientists, researchers, students, and practitioners a unique update on the latest advances in theory and a multitude of applications. It presents the peer-reviewed proceedings of the X International Conference on Complex Networks and their Applications (COMPLEX NETWORKS 2021). The carefully selected papers cover a wide range of theoretical topics such as network models and measures; community structure, network dynamics; diffusion, epidemics and spreading processes; resilience and control as well as all the main network applications, including social and political networks; networks in finance and economics; biological and neuroscience networks, and technological networks.

Author: Vladimir S. Korolyuk
Publisher: Springer Science & Business Media
ISBN: 9401110107
Category : Mathematics
Languages : en
Pages : 315

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Book Description
The evolution of systems in random media is a broad and fruitful field for the applica tions of different mathematical methods and theories. This evolution can be character ized by a semigroup property. In the abstract form, this property is given by a semigroup of operators in a normed vector (Banach) space. In the practically boundless variety of mathematical models of the evolutionary systems, we have chosen the semi-Markov ran dom evolutions as an object of our consideration. The definition of the evolutions of this type is based on rather simple initial assumptions. The random medium is described by the Markov renewal processes or by the semi Markov processes. The local characteristics of the system depend on the state of the ran dom medium. At the same time, the evolution of the system does not affect the medium. Hence, the semi-Markov random evolutions are described by two processes, namely, by the switching Markov renewal process, which describes the changes of the state of the external random medium, and by the switched process, i.e., by the semigroup of oper ators describing the evolution of the system in the semi-Markov random medium.

Author: Jaroslav Nešetřil
Publisher: Springer Science & Business Media
ISBN: 887642475X
Category : Mathematics
Languages : en
Pages : 612

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Book Description
In the tradition of EuroComb'01 (Barcelona), Eurocomb'03 (Prague), EuroComb'05 (Berlin), Eurocomb'07 (Seville), Eurocomb'09 (Bordeaux), and Eurocomb'11 (Budapest), this volume covers recent advances in combinatorics and graph theory including applications in other areas of mathematics, computer science and engineering. Topics include, but are not limited to: Algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, ordered sets, random methods, topological combinatorics.

Author: Alexander D. Kolesnik
Publisher: CRC Press
ISBN: 1000338797
Category : Mathematics
Languages : en
Pages : 265

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Book Description
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.

Author: Nasrullah Memon
Publisher: Springer Science & Business Media
ISBN: 3211094423
Category : Computers
Languages : en
Pages : 388

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Book Description
Terrorism is one of the serious threats to international peace and security that we face in this decade. No nation can consider itself immune from the dangers it poses, and no society can remain disengaged from the efforts to combat it. The termcounterterrorism refers to the techniques, strategies, and tactics used in the ?ght against terrorism. Counterterrorism efforts involve many segments of so- ety, especially governmental agencies including the police, military, and intelligence agencies (both domestic and international). The goal of counterterrorism efforts is to not only detect and prevent potential future acts but also to assist in the response to events that have already occurred. A terrorist cell usually forms very quietly and then grows in a pattern – sp- ning international borders, oceans, and hemispheres. Surprising to many, an eff- tive “weapon”, just as quiet – mathematics – can serve as a powerful tool to combat terrorism, providing the ability to connect the dots and reveal the organizational pattern of something so sinister. The events of 9/11 instantly changed perceptions of the wordsterrorist andn- work, especially in the United States. The international community was confronted with the need to tackle a threat which was not con?ned to a discreet physical - cation. This is a particular challenge to the standard instruments for projecting the legal authority of states and their power to uphold public safety. As demonstrated by the events of the 9/11 attack, we know that terrorist attacks can happen anywhere.