The YUIMA package is the first comprehensive R framework based on S4 classes and methods which allows for the simulation of stochastic differential equations driven by Wiener process, Lévy processes or fractional Brownian motion, as well as CARMA, COGARCH, and Point processes. The package performs various central statistical analyses such as quasi maximum likelihood estimation, adaptive Bayes estimation, structural change point analysis, hypotheses testing, asynchronous covariance estimation, lead-lag estimation, LASSO model selection, and so on. YUIMA also supports stochastic numerical analysis by fast computation of the expected value of functionals of stochastic processes through automatic asymptotic expansion by means of the Malliavin calculus. All models can be multidimensional, multiparametric or non parametric.The book explains briefly the underlying theory for simulation and inference of several classes of stochastic processes and then presents both simulation experiments and applications to real data. Although these processes have been originally proposed in physics and more recently in finance, they are becoming popular also in biology due to the fact the time course experimental data are now available. The YUIMA package, available on CRAN, can be freely downloaded and this companion book will make the user able to start his or her analysis from the first page.

Serving as the foundation for a one-semester course in stochastic processes for students familiar with elementary probability theory and calculus, Introduction to Stochastic Modeling, Fourth Edition, bridges the gap between basic probability and an intermediate level course in stochastic processes. The objectives of the text are to introduce students to the standard concepts and methods of stochastic modeling, to illustrate the rich diversity of applications of stochastic processes in the applied sciences, and to provide exercises in the application of simple stochastic analysis to realistic problems. New to this edition: Realistic applications from a variety of disciplines integrated throughout the text, including more biological applications Plentiful, completely updated problems Completely updated and reorganized end-of-chapter exercise sets, 250 exercises with answers New chapters of stochastic differential equations and Brownian motion and related processes Additional sections on Martingale and Poisson process Realistic applications from a variety of disciplines integrated throughout the text Extensive end of chapter exercises sets, 250 with answers Chapter 1-9 of the new edition are identical to the previous edition New! Chapter 10 - Random Evolutions New! Chapter 11- Characteristic functions and Their Applications

This book provides a self-contained account of continuous-parameter time series, starting with second-order models. Integration with respect to orthogonal increment processes, spectral theory and linear prediction are treated in detail. Lévy-driven models are incorporated, extending coverage to allow for infinite variance, a variety of marginal distributions and sample paths having jumps. The necessary theory of Lévy processes and integration of deterministic functions with respect to these processes is developed at length. Special emphasis is given to the analysis of continuous-time ARMA processes.

This text is an Elementary Introduction to Stochastic Processes in discrete and continuous time with an initiation of the statistical inference. The material is standard and classical for a first course in Stochastic Processes at the senior/graduate level (lessons 1-12). To provide students with a view of statistics of stochastic processes, three lessons (13-15) were added. These lessons can be either optional or serve as an introduction to statistical inference with dependent observations. Several points of this text need to be elaborated, (1) The pedagogy is somewhat obvious. Since this text is designed for a one semester course, each lesson can be covered in one week or so. Having in mind a mixed audience of students from different departments (Math ematics, Statistics, Economics, Engineering, etc.) we have presented the material in each lesson in the most simple way, with emphasis on moti vation of concepts, aspects of applications and computational procedures. Basically, we try to explain to beginners questions such as "What is the topic in this lesson?" "Why this topic?", "How to study this topic math ematically?". The exercises at the end of each lesson will deepen the stu dents' understanding of the material, and test their ability to carry out basic computations. Exercises with an asterisk are optional (difficult) and might not be suitable for homework, but should provide food for thought.

This book develops alternative methods to estimate the unknown parameters in stochastic volatility models, offering a new approach to test model accuracy. While there is ample research to document stochastic differential equation models driven by Brownian motion based on discrete observations of the underlying diffusion process, these traditional methods often fail to estimate the unknown parameters in the unobserved volatility processes. This text studies the second order rate of weak convergence to normality to obtain refined inference results like confidence interval, as well as nontraditional continuous time stochastic volatility models driven by fractional Levy processes. By incorporating jumps and long memory into the volatility process, these new methods will help better predict option pricing and stock market crash risk. Some simulation algorithms for numerical experiments are provided.

This textbook presents some basic stochastic processes, mainly Markov processes. It begins with a brief introduction to the framework of stochastic processes followed by the thorough discussion on Markov chains, which is the simplest and the most important class of stochastic processes. The book then elaborates the theory of Markov chains in detail including classification of states, the first passage distribution, the concept of periodicity and the limiting behaviour of a Markov chain in terms of associated stationary and long run distributions. The book first illustrates the theory for some typical Markov chains, such as random walk, gambler's ruin problem, Ehrenfest model and Bienayme-Galton-Watson branching process; and then extends the discussion when time parameter is continuous. It presents some important examples of a continuous time Markov chain, which include Poisson process, birth process, death process, birth and death processes and their variations. These processes play a fundamental role in the theory and applications in queuing and inventory models, population growth, epidemiology and engineering systems. The book studies in detail the Poisson process, which is the most frequently applied stochastic process in a variety of fields, with its extension to a renewal process. The book also presents important basic concepts on Brownian motion process, a stochastic process of historic importance. It covers its few extensions and variations, such as Brownian bridge, geometric Brownian motion process, which have applications in finance, stock markets, inventory etc. The book is designed primarily to serve as a textbook for a one semester introductory course in stochastic processes, in a post-graduate program, such as Statistics, Mathematics, Data Science and Finance. It can also be used for relevant courses in other disciplines. Additionally, it provides sufficient background material for studying inference in stochastic processes. The book thus fulfils the need of a concise but clear and student-friendly introduction to various types of stochastic processes.