Multidimensional Second Order Stochastic Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multidimensional Second Order Stochastic Processes write by Yichir Kakihara. This book was released on 1997. Multidimensional Second Order Stochastic Processes available in PDF, EPUB and Kindle. A research-expository treatment of infinite-dimensional nonstationary stochastic processes (or time series) on a locally compact abelian group is provided with this book. Stochastic measures and scalar or operator bimeasures are fully discussed.
Multidimensional Stochastic Processes as Rough Paths
Multidimensional Stochastic Processes as Rough Paths - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multidimensional Stochastic Processes as Rough Paths write by Peter K. Friz. This book was released on 2010-02-04. Multidimensional Stochastic Processes as Rough Paths available in PDF, EPUB and Kindle. Rough path analysis provides a fresh perspective on Ito's important theory of stochastic differential equations. Key theorems of modern stochastic analysis (existence and limit theorems for stochastic flows, Freidlin-Wentzell theory, the Stroock-Varadhan support description) can be obtained with dramatic simplifications. Classical approximation results and their limitations (Wong-Zakai, McShane's counterexample) receive 'obvious' rough path explanations. Evidence is building that rough paths will play an important role in the future analysis of stochastic partial differential equations and the authors include some first results in this direction. They also emphasize interactions with other parts of mathematics, including Caratheodory geometry, Dirichlet forms and Malliavin calculus. Based on successful courses at the graduate level, this up-to-date introduction presents the theory of rough paths and its applications to stochastic analysis. Examples, explanations and exercises make the book accessible to graduate students and researchers from a variety of fields.
Multidimensional Second Order Stochastic Processes
Multidimensional Second Order Stochastic Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multidimensional Second Order Stochastic Processes write by Yuichiro Kakihara. This book was released on 1997-02-27. Multidimensional Second Order Stochastic Processes available in PDF, EPUB and Kindle. This book provides a research-expository treatment of infinite-dimensional nonstationary stochastic processes or time series. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes and also the stationary class. Emphasis is on the use of functional, harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Readers may find that the covariance kernel analysis is emphasized and it reveals another aspect of stochastic processes. This book is intended not only for probabilists and statisticians, but also for communication engineers.
Hilbert And Banach Space-valued Stochastic Processes
Hilbert And Banach Space-valued Stochastic Processes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Hilbert And Banach Space-valued Stochastic Processes write by Yuichiro Kakihara. This book was released on 2021-07-29. Hilbert And Banach Space-valued Stochastic Processes available in PDF, EPUB and Kindle. This is a development of the book entitled Multidimensional Second Order Stochastic Processes. It provides a research expository treatment of infinite-dimensional stationary and nonstationary stochastic processes or time series, based on Hilbert and Banach space-valued second order random variables. Stochastic measures and scalar or operator bimeasures are fully discussed to develop integral representations of various classes of nonstationary processes such as harmonizable, V-bounded, Cramér and Karhunen classes as well as the stationary class. A new type of the Radon-Nikodým derivative of a Banach space-valued measure is introduced, together with Schauder basic measures, to study uniformly bounded linearly stationary processes.Emphasis is on the use of functional analysis and harmonic analysis as well as probability theory. Applications are made from the probabilistic and statistical points of view to prediction problems, Kalman filter, sampling theorems and strong laws of large numbers. Generalizations are made to consider Banach space-valued stochastic processes to include processes of pth order for p ≥ 1. Readers may find that the covariance kernel is always emphasized and reveals another aspect of stochastic processes.This book is intended not only for probabilists and statisticians, but also for functional analysts and communication engineers.
Stochastic Processes and Applications
Stochastic Processes and Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Processes and Applications write by Grigorios A. Pavliotis. This book was released on 2014-11-19. Stochastic Processes and Applications available in PDF, EPUB and Kindle. This book presents various results and techniques from the theory of stochastic processes that are useful in the study of stochastic problems in the natural sciences. The main focus is analytical methods, although numerical methods and statistical inference methodologies for studying diffusion processes are also presented. The goal is the development of techniques that are applicable to a wide variety of stochastic models that appear in physics, chemistry and other natural sciences. Applications such as stochastic resonance, Brownian motion in periodic potentials and Brownian motors are studied and the connection between diffusion processes and time-dependent statistical mechanics is elucidated. The book contains a large number of illustrations, examples, and exercises. It will be useful for graduate-level courses on stochastic processes for students in applied mathematics, physics and engineering. Many of the topics covered in this book (reversible diffusions, convergence to equilibrium for diffusion processes, inference methods for stochastic differential equations, derivation of the generalized Langevin equation, exit time problems) cannot be easily found in textbook form and will be useful to both researchers and students interested in the applications of stochastic processes.
