Stochastic Processes and Applications

This book highlights the latest advances in stochastic processes, probability theory, mathematical statistics, engineering mathematics and algebraic structures, focusing on mathematical models, structures, concepts, problems and computational methods and algorithms important in modern technology, engineering and natural sciences applications.

It comprises selected, high-quality, refereed contributions from various large research communities in modern stochastic processes, algebraic structures and their interplay and applications. The chapters cover both theory and applications, illustrated by numerous figures, schemes, algorithms, tables and research results to help readers understand the material and develop new mathematical methods, concepts and computing applications in the future.

Presenting new methods and results, reviews of cutting-edge research, and open problems and directions for future research, the book serves as a source of inspiration for a broadspectrum of researchers and research students in probability theory and mathematical statistics, applied algebraic structures, applied mathematics and other areas of mathematics and applications of mathematics.

The book is based on selected contributions presented at the International Conference on Stochastic Processes and Algebraic Structures From Theory Towards Applications (SPAS2017) to mark Professor Dmitrii Silvestrov's 70th birthday and his 50 years of fruitful service to mathematics, education and international cooperation, which was held at Mälardalen University in Västerås and Stockholm University, Sweden, in October 2017.

Discusses both theory and applications Features mathematical methods and models in applications to important problems of science and engineering Includes high-quality, peer-reviewed contributed chapters, which present various new methods and results, reviews of up to date research and open directions and problems for future research Serves as a source of inspiration for a broad spectrum of researchers and research students in mathematics and its applications in other subjects

Inhalt
Part I Stochastic Processes: Silvestrov Dmitrii: A Journey in the World of Stochastic Processes.- Silvestrov Dmitrii: Individual Ergodic Theorems for Perturbed Alternating Regenerative Processes.- Krasnitskiy Sergey and Kurchenko Oleksandr: On Baxter Type Theorems for Generalized Random Gaussian Fields.- Bajja Salwa, Es-Sebaiy Khalifa, and Viitasaari Lauri: Limit Theorems for Quadratic Variations of the LeiNualart Process.- Mishura Yuliya, Ralchenko Kostiantyn, and Shklyar Sergiy: Parameter Estimation for Gaussian Processes with Application to the Model with two Independent Fractional Brownian Motions.- Rakhimova Gulnoza: Application of Limit Theorems for Superposition of Random Functions to Sequential Estimation.- Morlanes José Igor and Andreev Andriy: On Simulation of a Fractional Ornstein-Uhlenbeck Process of the Second Kind by the Circulant Embedding Method.- Lindensjö Kristoffer: Constructive Martingale Representation in Functional Itô Calculus: a Local Martingale Extension.- Malyarenko Anatoliy and Ostoja-Starzewski Martin: Random Fields Related to the Symmetry Classes of Second-Order Symmetric Tensors.- Part II Applications of Stochastic Processes: Silvestrov Dmitrii, Petersson Mikael, and Hössjer Ola: Nonlinearly Perturbed Birth-Death-Type Models.- Hössjer Ola, Bechly Günter, and Gauger Ann: Phase-type Distribution Approximations of the Waiting Time Until Coordinated Mutations Get Fixed in a Population.- Spricer Kristoffer and Trapman Pieter: Characterizing the Initial Phase of Epidemic Growth on some Empirical Networks.- Boguslavskaya Elena, Mishura Yuliya, and Shevchenko Georgiy: Replication of Wiener-Transformable Stochastic Processes with Application to Financial Markets with Memory.- D'Amico Guglielmo, Gismondi Fulvio, and Petroni Filippo: A New Approach to the Modeling of Financial Volumes.- Abola Benard, Biganda Pitos Seleka, Engström Christopher, Mango John Magero, Kakuba Godwin, and Silvestrov Sergei: PageRank in Evolving Tree Graphs.- Biganda Pitos Seleka, Abola Benard, Engström Christopher, Mango John Magero, Kakuba Godwin, and Silvestrov Sergei: Traditional and Lazy PageRanks for a Line of Nodes Connected with Complete Graphs.- Malmberg Hannes and Hössjer Ola : Continuous Approximations of Discrete Choice Models Using Point Process Theory.- Faybishenko Boris, Molz Fred, and Agarwal Deborah: Nonlinear Dynamics Simulations of Microbial Ecological Processes: Model, Diagnostic Parameters of Deterministic Chaos, and Sensitivity Analysis.- **Index.