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Discrete Time Approximations And Limit Theorems

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Discrete Time Approximations And Limit Theorems

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Author : Yuliya Mishura
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-10-25

Discrete Time Approximations And Limit Theorems written by Yuliya Mishura and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-25 with Mathematics categories.

Financial market modeling is a prime example of a real-life application of probability theory and stochastics. This authoritative book discusses the discrete-time approximation and other qualitative properties of models of financial markets, like the Black-Scholes model and its generalizations, offering in this way rigorous insights on one of the most interesting applications of mathematics nowadays.

Discrete Time Approximations And Limit Theorems

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Author : Yuliya S. Mishura
language : en
Publisher:
Release Date : 2021-06-10

Discrete Time Approximations And Limit Theorems written by Yuliya S. Mishura and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-10 with categories.

Approximation Methods And Analytical Modeling Using Partial Differential Equations

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Author : Tamara Fastovska
language : en
Publisher: Frontiers Media SA
Release Date : 2025-03-28

Approximation Methods And Analytical Modeling Using Partial Differential Equations written by Tamara Fastovska and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-28 with Science categories.

Adequate mathematical modeling is the key to success for many real-world projects in engineering, medicine, and other applied areas. As soon as an appropriate mathematical model is developed, it can be comprehensively analyzed by a broad spectrum of available mathematical methods. For example, compartmental models are widely used in mathematical epidemiology to describe the dynamics of infectious diseases and in mathematical models of population genetics. While the existence of an optimal solution under certain condition can be often proved rigorously, this does not always mean that such a solution is easy to implement in practice. Finding a reasonable approximation can in itself be a challenging research problem. This Research Topic is devoted to modeling, analysis, and approximation problems whose solutions exploit and explore the theory of partial differential equations. It aims to highlight new analytical tools for use in the modeling of problems arising in applied sciences and practical areas. Researchers are invited to submit articles that investigate the qualitative behavior of weak solutions (removability conditions for singularities), the dependence of the local asymptotic property of these solutions on initial and boundary data, and also the existence of solutions. Contributors are particularly encouraged to focus on anisotropic models: analyzing the preconditions on the strength of the anisotropy, and comparing the analytical estimates for the growth behavior of the solutions near the singularities with the observed growth in numerical simulations. The qualitative analysis and analytical results should be confirmed by the numerically observed solution behavior.

The Mathematics Of Internet Congestion Control

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Author : Rayadurgam Srikant
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

The Mathematics Of Internet Congestion Control written by Rayadurgam Srikant and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

Congestion control algorithms were implemented for the Internet nearly two decades ago, but mathematical models of congestion control in such a large-scale network are relatively new. This text presents models for the development of new protocols that can help make Internet data transfers virtually loss- and delay-free. Introduced are tools from optimization, control theory, and stochastic processes integral to the study of congestion control algorithms. Intended for graduate students and researchers in systems theory and computer science, the text assumes basic knowledge of first-year, graduate-level control theory, optimization, and stochastic processes, but the key prerequisites are summarized in an appendix for quick reference. The work's wide range of applications to the study of both new and existing protocols and control algorithms make the book of interest to researchers and students concerned with many aspects of large-scale information flow on the Internet.

Probabilistic Symmetries And Invariance Principles

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Author : Olav Kallenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-12-15

Probabilistic Symmetries And Invariance Principles written by Olav Kallenberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-15 with Mathematics categories.

"This is the first comprehensive treatment of the three basic symmetries of probability theory - contractability, exchangeability, and rotatability - defined as invariance in distribution under contractions, permutations, and rotations. Most chapters require only some basic, graduate level probability theory, and should be accessible to any serious researchers and graduate students in probability and statistics. Parts of the book may also be of interest to pure and applied mathematicians in other areas. The exposition is formally self-contained, with detailed references provided for any deeper facts from real analysis or probability used in the book."--Jacket.

Optimal Input Signals For Parameter Estimation

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Author : Ewaryst Rafajłowicz
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2022-03-07

Optimal Input Signals For Parameter Estimation written by Ewaryst Rafajłowicz and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-07 with History categories.

The aim of this book is to provide methods and algorithms for the optimization of input signals so as to estimate parameters in systems described by PDE’s as accurate as possible under given constraints. The optimality conditions have their background in the optimal experiment design theory for regression functions and in simple but useful results on the dependence of eigenvalues of partial differential operators on their parameters. Examples are provided that reveal sometimes intriguing geometry of spatiotemporal input signals and responses to them. An introduction to optimal experimental design for parameter estimation of regression functions is provided. The emphasis is on functions having a tensor product (Kronecker) structure that is compatible with eigenfunctions of many partial differential operators. New optimality conditions in the time domain and computational algorithms are derived for D-optimal input signals when parameters of ordinary differential equations are estimated. They are used as building blocks for constructing D-optimal spatio-temporal inputs for systems described by linear partial differential equations of the parabolic and hyperbolic types with constant parameters. Optimality conditions for spatially distributed signals are also obtained for equations of elliptic type in those cases where their eigenfunctions do not depend on unknown constant parameters. These conditions and the resulting algorithms are interesting in their own right and, moreover, they are second building blocks for optimality of spatio-temporal signals. A discussion of the generalizability and possible applications of the results obtained is presented.

Probability Methods For Approximations In Stochastic Control And For Elliptic Equations

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Author : Kushner
language : en
Publisher: Academic Press
Release Date : 1977-04-14

Probability Methods For Approximations In Stochastic Control And For Elliptic Equations written by Kushner and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-04-14 with Computers categories.

Probability Methods for Approximations in Stochastic Control and for Elliptic Equations

Brownian Motion

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Author : René L. Schilling
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-09-07

Brownian Motion written by René L. Schilling and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-07 with Mathematics categories.

Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''.

Inference For Diffusion Processes

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Author : Christiane Fuchs
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-18

Inference For Diffusion Processes written by Christiane Fuchs and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-18 with Mathematics categories.

Diffusion processes are a promising instrument for realistically modelling the time-continuous evolution of phenomena not only in the natural sciences but also in finance and economics. Their mathematical theory, however, is challenging, and hence diffusion modelling is often carried out incorrectly, and the according statistical inference is considered almost exclusively by theoreticians. This book explains both topics in an illustrative way which also addresses practitioners. It provides a complete overview of the current state of research and presents important, novel insights. The theory is demonstrated using real data applications.

Stochastic Approximation And Recursive Algorithms And Applications

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Author : Harold Kushner
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Stochastic Approximation And Recursive Algorithms And Applications written by Harold Kushner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.

In recent years algorithms of the stochastic approximation type have found applications in new and diverse areas, and new techniques have been developed for proofs of convergence and rate of convergence. The actual and potential applications in signal processing have exploded. New challenges have arisen in applications to adaptive control. This book presents a thorough coverage of the ODE method used to analyze these algorithms.

Discrete Time Approximations And Limit Theorems

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