Tag: Stochastic

Free Download Stochastic Processes: A Survey of the Mathematical Theory by John Lamperti
English | PDF | 1977 | 284 Pages | ISBN : 0387902759 | 18.5 MB
This book is the result of lectures which I gave dur ing the academic year 1972-73 to third-year students a~ Aarhus University in Denmark. The purpose of the book, as of the lectures, is to survey some of the main themes in the modern theory of stochastic processes. In my previous book Probability: ! survey of the mathe matical theory I gave a short overview of "classical" proba bility mathematics, concentrating especially on sums of inde pendent random variables. I did not discuss specific appli cations of the theory; I did strive for a spirit friendly to application by coming to grips as fast as I could with the major problems and techniques and by avoiding too high levels of abstraction and completeness. At the same time, I tried to make the proofs both rigorous and motivated and to show how certain results have evolved rather than just presenting them in polished final form. The same remarks apply to this book, at least as a statement of intentions, and it can serve as a sequel to the earlier one continuing the story in the same style and spirit. The contents of the present book fall roughly into two parts. The first deals mostly with stationary processes, which provide the mathematics for describing phenomena in a steady state overall but subject to random fluctuations. Chapter 4 is the heart of this part.

Free Download Quantum and Stochastic Mathematical Physics: Sergio Albeverio, Adventures of a Mathematician, Verona, Italy, March 25-29, 2019 by Astrid Hilbert, Elisa Mastrogiacomo, Sonia Mazzucchi, Barbara Rüdiger, Stefania Ugolini
English | PDF,EPUB | 2023 | 390 Pages | ISBN : 3031140303 | 27.3 MB
Sergio Albeverio gave important contributions to many fields ranging from Physics to Mathematics, while creating new research areas from their interplay. Some of them are presented in this Volume that grew out of the Random Transformations and Invariance in Stochastic Dynamics Workshop held in Verona in 2019. To understand the theory of thermo- and fluid-dynamics, statistical mechanics, quantum mechanics and quantum field theory, Albeverio and his collaborators developed stochastic theories having strong interplays with operator theory and functional analysis. His contribution to the theory of (non Gaussian)-SPDEs, the related theory of (pseudo-)differential operators, and ergodic theory had several impacts to solve problems related, among other topics, to thermo- and fluid dynamics. His scientific works in the theory of interacting particles and its extension to configuration spaces lead, e.g., to the solution of open problems in statistical mechanics and quantum field theory. Together with Raphael Hoegh Krohn he introduced the theory of infinite dimensional Dirichlet forms, which nowadays is used in many different contexts, and new methods in the theory of Feynman path integration. He did not fear to further develop different methods in Mathematics, like, e.g., the theory of non-standard analysis and p-adic numbers.

Free Download A Course of Stochastic Analysis by Alexander Melnikov
English | PDF (True)/EPUB | 2023 | 214 Pages | ISBN : 3031253256 | 2.6 MB
The main subject of the book is stochastic analysis and its various applications to mathematical finance and statistics of random processes. The main purpose of the book is to present, in a short and sufficiently self-contained form, the methods and results of the contemporary theory of stochastic analysis and to show how these methods and results work in mathematical finance and statistics of random processes. The book can be considered as a textbook for both senior undergraduate and graduate courses on this subject. The book can be helpful for undergraduate and graduate students, instructors and specialists on stochastic analysis and its applications.

Free Download Stochastic Processes by Rodney Coleman
English | PDF | 1974 | 99 Pages | ISBN : 0045190178 | 5.95 MB
The word stochastic is jargon for random. A stochastic process is a system which evolves in time while undergoing chance fluctuations. We can describe such a system by defining a family of random variables, {Xt}’ where Xt measures, at time t, the aspect of the system which is of interest. For example, X t might be the number of customers in a queue at time t. As time passes, customers will arrive and leave, and so the value of Xt will change. At any time t, Xt takes one of the values 0, 1,2, … ; and t can be any value in a subset of ( – 00, 00), the infinite past to the infinite future. If we observe the queue continuously, and customers arrive one at a time to be served by a single server, then, when a customer arrives, the value of Xt’ the queue size, increases by one, and when a customer departs after being served, X t decreases by one (Figure 1.1).

Free Download Stochastic Processes and Calculus: An Elementary Introduction with Applications by Uwe Hassler
English | EPUB (True) | 2016 | 398 Pages | ISBN : 3319234277 | 4.64 MB
This textbook gives a comprehensive introduction to stochastic processes and calculus in the fields of finance and economics, more specifically mathematical finance and time series econometrics. Over the past decades stochastic calculus and processes have gained great importance, because they play a decisive role in the modeling of financial markets and as a basis for modern time series econometrics. Mathematical theory is applied to solve stochastic differential equations and to derive limiting results for statistical inference on nonstationary processes.

Free Download Stochastic Processes Problems and Solutions by L. Takács
English | PDF | 1966 | 143 Pages | ISBN : 0412203405 | 8.3 MB
It is not so very long ago that up-to-date text-books on statistics were almost non-existent. In the last few decades this deficiency has largely been remedied, but in order to cope with a broad and rapidly expanding subject many of these books have been fairly big and expensive. The success of Methuen’s existing series of monographs, in physics or in biology, for example, stresses the value of short inexpensive treatments to which a student can turn for an introduc tion to, or a revision of, specialised topics. In this new Methuen series the still-growing importance of prob ability theory in its applied aspects has been recognised by coupling together Probability and Statistics; and included in the series are some of the newer applications of probability theory to stochastic models in various fields, storage and service problems, ‘Monte Carlo’ techniques, etc. , as well as monographs on particular statistical topics.