3 edition of Random Series and Stochastic Integrals found in the catalog.
Random Series and Stochastic Integrals
by Birkhauser Boston
Written in English
|The Physical Object|
An α-stable stochastic process is a random element whose finite-dimensional distributions are α-stable. It is used to introduce the notion of α-stable stochastic integrals. It is convenient to view these integrals as α-stable stochastic processes parameterized by their integrands. This chapter develops some basic properties of stable : Gennady Samorodnitsky, Murad S. Taqqu. Stochastic refers to a randomly determined process. The word first appeared in English to describe a mathematical object called a stochastic process, but now in mathematics the terms stochastic process and random process are considered interchangeable. The word, with its current definition meaning random, came from German, but it originally came from Greek .
Part of the Applications of Mathematics book series (SMAP, volume 6) Log in to check access. Buy eBook. USD Application of filtering equations to problems of statistics of random sequences. R. S. Liptser, A. N. Shiryayev. Pages Stieltjes stochastic integrals. R. S. Liptser, A. N. Shiryayev. Pages The book is devoted to the structural analysis of vector and random (or both) valued countably additive measures, and used for integral representations of random fields. attention is given to Bochner's boundedness principle and Grothendieck's representation unifying and simplyfying stochastic integrations. Several stationary aspects.
1. Stable random variables on the real line 2. Multivariate stable distributions 3. Stable random processes and stochastic integrals 4. Dependence Structures of Multivariate Stable Distributions 5. Non-linear regression 6. Complex stable stochastic integrals and harmonizable processes 7. Self-similar processes 8. Chentsov random fields 9. The theory of stochastic integration, also called the Ito calculus, has a large spectrum of applications in virtually every scientific area involving random functions, but it can be a very difficult subject for people without much mathematical background.
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This book studies the foundations of the theory of linear and nonlinear forms in single and multiple random variables including the single and multiple random series and stochastic integrals, both Gaussian and non-Gaussian. This subject is intimately connected with a number of classical problems of probability theory such as the summation of independent random.
Get this from a library. Random series and stochastic integrals: single and multiple. [Stanisław Kwapień; Wojbor Andrzej Woyczyński].
This book studies the foundations of the theory of linear and nonlinear forms in single and multiple random variables including the single and multiple random series and stochastic integrals, both Gaussian and non-Gaussian.
This subject is intimately connected with a number of classical problems of. This book studies the foundations of the theory of linear and nonlinear forms in single and multiple random variables including the single and multiple random series and stochastic integrals, both Read more.
Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Stochastic Calculus and Stochastic Models focuses on the properties, functions, and applications of stochastic integrals. The publication first ponders on stochastic integrals, existence of stochastic integrals, and continuity, chain rule, and substitution.
Publisher Summary. This chapter defines various modes of stochastic convergence of the sequences of random variables. This enables the consideration of infinite series of random variables and to say that an infinite series of random variables is convergent (in the sense of a particular stochastic convergence concept) if the sequence of its partial sums converges.
Path Integrals in Physics: Volume I, Stochastic Processes and Quantum Mechanics presents the fundamentals of path integrals, both the Wiener and Feynman type, and their many applications in physics.
Accessible to a broad community of theoretical physicists, the book deals with systems possessing a infinite number of degrees in by: Stochastic Integrals discusses one area of diffusion processes: the differential and integral calculus based upon the Brownian motion.
The book reviews Gaussian families, construction of the Brownian motion, the simplest properties of the Brownian motion, Martingale inequality, and the law of the iterated Edition: 1. This is a textbook for advanced undergraduate students and beginning graduate students in applied mathematics.
It presents the basic mathematical foundations of stochastic analysis (probability theory and stochastic processes) as well as some important practical tools and applications (e.g., the connection with differential equations, numerical methods, path.
This book sheds new light on stochastic calculus, the branch of mathematics that is most widely applied in financial engineering and mathematical finance.
The first book to introduce pathwise formulae for the stochastic integral, it provides a simple but rigorous treatment of the subject, including a range of advanced topics.
A ground-breaking and practical treatment of probability and stochastic processes. A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics.
Setting aside the classical theory of probability measure spaces, the book utilizes. Books shelved as stochastic-processes: Introduction to Stochastic Processes by Gregory F. Lawler, Adventures in Stochastic Processes by Sidney I. Resnick.
At the end of s and the beginning of s, when the Russian version of this book was written, the 'general theory of random processes' did not operate widely with such notions as semimartingale, stochastic integral with respect to semimartingale, the ItO formula for semimartingales, etc.
At that time in stochastic calculus (theory of martingales), the main. Stochastic calculus is a branch of mathematics that operates on stochastic allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes.
It is used to model systems that behave randomly. The best-known stochastic process to which stochastic calculus is applied is the Wiener process (named in.
Random Series and Stochastic Integrals: Single and Multiple (Stanislaw Kwapien and Wojbar A. Woyczynski)Author: Philip Protter. () Approximation of Multiple Stochastic Integrals and Its Application to Stochastic Differential Equations.
Nonlinear Analysis: Theory, Methods & ApplicationsJ. Cited by: Integral of a random function. Ask Question Asked 7 years, 7 months ago. Browse other questions tagged stochastic-integrals random-functions random-variables or ask your own question. Will reading the same book in two languages confuse my daughter.
If Xis a random variable, then its expectation, E[X] can be thought of as the best guess for X given no information about the result of the trial. A conditional expectation can be considered as the best guess given some but not total information.
Let X 1;X 2;be random variables which we think of as a time series with the data arriving one at File Size: KB.
In probability theory and related fields, a stochastic or random process is a mathematical object usually defined as a family of random ically, the random variables were associated with or indexed by a set of numbers, usually viewed as points in time, giving the interpretation of a stochastic process representing numerical values of some system randomly changing over.
Chapter 5 (Expansions of Iterated Ito and Stratonovich Stochastic Integrals, Based on Multiple and Iterated Fourier Series, Converging in the Mean and. The book is a collection of 25 articles () which are devoted to the problem of strong (mean-square) approximation of iterated Ito and Stratonovich stochastic integrals .This three-part treatment introduces the basic facts of the theory of random processes and constructs the auxiliary apparatus of stochastic integrals.
Additional topics include the theory of stochastic differential equations and various limit theorems connected with the convergence of a sequence of Markov chains to a Markov process with continuous time.
edition.Both an introduction and a basic reference text on non-Gaussian stable models, for graduate students and practitioners. Assuming only a first-year graduate course in probability, it includes material which has only recently appeared in journals and unpublished materials.
Each chapter begins with a brief overview and concludes with a range of exercises at varying levels of difficulty.