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Set-Valued Stochastic Integrals and Applications

Author : Michał Kisielewicz

Publisher : Springer Nature

Page : 287 pages

File Size : 48,16 MB

Release : 2020-06-26

Category : Mathematics

ISBN : 3030403297

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Book Description

This book is among the first concise presentations of the set-valued stochastic integration theory as well as its natural applications, as well as the first to contain complex approach theory of set-valued stochastic integrals. Taking particular consideration of set-valued Itô , set-valued stochastic Lebesgue, and stochastic Aumann integrals, the volume is divided into nine parts. It begins with preliminaries of mathematical methods that are then applied in later chapters containing the main results and some of their applications, and contains many new problems. Methods applied in the book are mainly based on functional analysis, theory of probability processes, and theory of set-valued mappings. The volume will appeal to students of mathematics, economics, and engineering, as well as to mathematics professionals interested in applications of the theory of set-valued stochastic integrals.



Stochastic Differential Inclusions and Applications

Author : Michał Kisielewicz

Publisher : Springer Science & Business Media

Page : 295 pages

File Size : 22,47 MB

Release : 2013-06-12

Category : Mathematics

ISBN : 146146756X

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Book Description

​This book aims to further develop the theory of stochastic functional inclusions and their applications for describing the solutions of the initial and boundary value problems for partial differential inclusions. The self-contained volume is designed to introduce the reader in a systematic fashion, to new methods of the stochastic optimal control theory from the very beginning. The exposition contains detailed proofs and uses new and original methods to characterize the properties of stochastic functional inclusions that, up to the present time, have only been published recently by the author. The work is divided into seven chapters, with the first two acting as an introduction, containing selected material dealing with point- and set-valued stochastic processes, and the final two devoted to applications and optimal control problems. The book presents recent and pressing issues in stochastic processes, control, differential games, optimization and their application in finance, manufacturing, queueing networks, and climate control. Written by an award-winning author in the field of stochastic differential inclusions and their application to control theory, This book is intended for students and researchers in mathematics and applications; particularly those studying optimal control theory. It is also highly relevant for students of economics and engineering. The book can also be used as a reference on stochastic differential inclusions. Knowledge of select topics in analysis and probability theory are required.



Nonlinear Mathematics for Uncertainty and its Applications

Author : Shoumei Li

Publisher : Springer Science & Business Media

Page : 708 pages

File Size : 37,71 MB

Release : 2011-07-21

Category : Technology & Engineering

ISBN : 364222833X

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Book Description

This volume is a collection of papers presented at the international conference on Nonlinear Mathematics for Uncertainty and Its Applications (NLMUA2011), held at Beijing University of Technology during the week of September 7--9, 2011. The conference brought together leading researchers and practitioners involved with all aspects of nonlinear mathematics for uncertainty and its applications. Over the last fifty years there have been many attempts in extending the theory of classical probability and statistical models to the generalized one which can cope with problems of inference and decision making when the model-related information is scarce, vague, ambiguous, or incomplete. Such attempts include the study of nonadditive measures and their integrals, imprecise probabilities and random sets, and their applications in information sciences, economics, finance, insurance, engineering, and social sciences. The book presents topics including nonadditive measures and nonlinear integrals, Choquet, Sugeno and other types of integrals, possibility theory, Dempster-Shafer theory, random sets, fuzzy random sets and related statistics, set-valued and fuzzy stochastic processes, imprecise probability theory and related statistical models, fuzzy mathematics, nonlinear functional analysis, information theory, mathematical finance and risk managements, decision making under various types of uncertainty, and others.



Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables

Author : Shoumei Li

Publisher : Springer Science & Business Media

Page : 399 pages

File Size : 36,66 MB

Release : 2013-04-17

Category : Mathematics

ISBN : 9401599327

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Book Description

After the pioneering works by Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall {1974) and Matheron {1975). It is well known that the theory of set-valued random variables is a natural extension of that of general real-valued random variables or random vectors. However, owing to the topological structure of the space of closed sets and special features of set-theoretic operations ( cf. Beer [27]), set-valued random variables have many special properties. This gives new meanings for the classical probability theory. As a result of the development in this area in the past more than 30 years, the theory of set-valued random variables with many applications has become one of new and active branches in probability theory. In practice also, we are often faced with random experiments whose outcomes are not numbers but are expressed in inexact linguistic terms.



Proceeding of 2021 International Conference on Wireless Communications, Networking and Applications

Author : Zhihong Qian

Publisher : Springer Nature

Page : 1251 pages

File Size : 12,32 MB

Release : 2022-07-12

Category : Technology & Engineering

ISBN : 9811924562

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Book Description

This open access proceedings includes original, unpublished, peer-reviewed research papers from the International Conference on Wireless Communications, Networking and Applications (WCNA2021), held in Berlin, Germany on December 17-19th, 2021. The topics covered include but are not limited to wireless communications, networking and applications.The papers showcased here share the latest findings on methodologies, algorithms and applications in communication and network, making the book a valuable asset for professors, researchers, engineers, and university students alike. This is an open access book.



Soft Methods for Handling Variability and Imprecision

Author : Didier Dubois

Publisher : Springer Science & Business Media

Page : 436 pages

File Size : 36,72 MB

Release : 2008-10-01

Category : Mathematics

ISBN : 3540850279

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Book Description

Probability theory has been the only well-founded theory of uncertainty for a long time. It was viewed either as a powerful tool for modelling random phenomena, or as a rational approach to the notion of degree of belief. During the last thirty years, in areas centered around decision theory, artificial intelligence and information processing, numerous approaches extending or orthogonal to the existing theory of probability and mathematical statistics have come to the front. The common feature of those attempts is to allow for softer or wider frameworks for taking into account the incompleteness or imprecision of information. Many of these approaches come down to blending interval or fuzzy interval analysis with probabilistic methods. This book gathers contributions to the 4th International Conference on Soft methods in Probability and Statistics. Its aim is to present recent results illustrating such new trends that enlarge the statistical and uncertainty modeling traditions, towards the handling of incomplete or subjective information. It covers a broad scope ranging from philosophical and mathematical underpinnings of new uncertainty theories, with a stress on their impact in the area of statistics and data analysis, to numerical methods and applications to environmental risk analysis and mechanical engineering. A unique feature of this collection is to establish a dialogue between fuzzy random variables and imprecise probability theories.



Intelligent Systems: Models and Applications

Author : Endre Pap

Publisher : Springer Science & Business Media

Page : 342 pages

File Size : 37,1 MB

Release : 2012-10-20

Category : Technology & Engineering

ISBN : 364233959X

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Book Description

The theory and applications of intelligent systems is today an important field of research. This book is an up-to-date collection of seventeen chapters, written by recognized experts in the field. In an introductory mathematical foundations part an overview of generalizations of the integral inequalities for nonadditive integrals and a construction of the General Prioritized Fuzzy Satisfaction Problem is given. Then different aspects of robotics are presented, such as the differences between human beings and robots, the motion of bipedal humanoid robots, and an evaluation of different autonomous quadrotor flight controllers. Also Fuzzy Systems are presented by a model of basic planar imprecise geometric objects allowing various applications in image analysis , GIS, and robotics, as well as a type-2 fuzzy logic in a software library for developing perceptual computers, and a two--degree--of--freedom speed control solutions for a brushless Direct Current motor. The book also presents recent applications in medicine such as a Virtual Doctor System, methods for a face to face human machine interaction, and an emotion estimation, with applications for multiple diseases and the effect of the applied therapy. The last part of the book covers different applications in transportation, network monitoring, and localization of pedestrians in images.



Combining Soft Computing and Statistical Methods in Data Analysis

Author : Christian Borgelt

Publisher : Springer Science & Business Media

Page : 640 pages

File Size : 29,52 MB

Release : 2010-10-12

Category : Technology & Engineering

ISBN : 3642147461

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Book Description

Over the last forty years there has been a growing interest to extend probability theory and statistics and to allow for more flexible modelling of imprecision, uncertainty, vagueness and ignorance. The fact that in many real-life situations data uncertainty is not only present in the form of randomness (stochastic uncertainty) but also in the form of imprecision/fuzziness is but one point underlining the need for a widening of statistical tools. Most such extensions originate in a "softening" of classical methods, allowing, in particular, to work with imprecise or vague data, considering imprecise or generalized probabilities and fuzzy events, etc. About ten years ago the idea of establishing a recurrent forum for discussing new trends in the before-mentioned context was born and resulted in the first International Conference on Soft Methods in Probability and Statistics (SMPS) that was held in Warsaw in 2002. In the following years the conference took place in Oviedo (2004), in Bristol (2006) and in Toulouse (2008). In the current edition the conference returns to Oviedo. This edited volume is a collection of papers presented at the SMPS 2010 conference held in Mieres and Oviedo. It gives a comprehensive overview of current research into the fusion of soft methods with probability and statistics.



Mathematics—Advances in Research and Application: 2012 Edition

Author :

Publisher : ScholarlyEditions

Page : 1637 pages

File Size : 49,63 MB

Release : 2012-12-26

Category : Mathematics

ISBN : 1464990719

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Book Description

Mathematics—Advances in Research and Application: 2012 Edition is a ScholarlyEditions™ eBook that delivers timely, authoritative, and comprehensive information about Mathematics. The editors have built Mathematics—Advances in Research and Application: 2012 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about Mathematics in this eBook to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Mathematics—Advances in Research and Application: 2012 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.



Theory of Random Sets

Author : Ilya Molchanov

Publisher : Springer

Page : 688 pages

File Size : 11,80 MB

Release : 2017-12-14

Category : Mathematics

ISBN : 144717349X

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Book Description

This monograph, now in a thoroughly revised second edition, offers the latest research on random sets. It has been extended to include substantial developments achieved since 2005, some of them motivated by applications of random sets to econometrics and finance. The present volume builds on the foundations laid by Matheron and others, including the vast advances in stochastic geometry, probability theory, set-valued analysis, and statistical inference. It shows the various interdisciplinary relationships of random set theory within other parts of mathematics, and at the same time fixes terminology and notation that often vary in the literature, establishing it as a natural part of modern probability theory and providing a platform for future development. It is completely self-contained, systematic and exhaustive, with the full proofs that are necessary to gain insight. Aimed at research level, Theory of Random Sets will be an invaluable reference for probabilists; mathematicians working in convex and integral geometry, set-valued analysis, capacity and potential theory; mathematical statisticians in spatial statistics and uncertainty quantification; specialists in mathematical economics, econometrics, decision theory, and mathematical finance; and electronic and electrical engineers interested in image analysis.