Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 2
Book Description
The subjects of this research are certain probabilistic properties of real and vector valued random functions X(t), where t is a generalized time parameter taking values in a subset T of Euclidean space. The distributions of three functionals of the random function X are studied. For any Borel set A in the range, the sojourn time of X in A is defined as the measure of the subset of the points t in T such that X(t) belongs to A. The self-intersection set of X is the subset of the set of points (s, t) in the product space of T such that s = t and X(s) = X(t). Finally, for a real valued random function X, the extreme value is the functional equal to the maximum value of X on the domain T. The research is concerned with the determination of the distributions of these functionals under various hypotheses about the probabilistic structure of X. It is assumed here that the random function is Gaussian or Markovian. Stochastic process, Extreme value, Sojourn time, Local time, Limiting distribution, Self- intersections of paths, Gaussian process, Markov process.
Sojourns, Extremes, and Self-Intersections of Stochastic Processes
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages : 2
Book Description
The subjects of this research are certain probabilistic properties of real and vector valued random functions X(t), where t is a generalized time parameter taking values in a subset T of Euclidean space. The distributions of three functionals of the random function X are studied. For any Borel set A in the range, the sojourn time of X in A is defined as the measure of the subset of the points t in T such that X(t) belongs to A. The self-intersection set of X is the subset of the set of points (s, t) in the product space of T such that s = t and X(s) = X(t). Finally, for a real valued random function X, the extreme value is the functional equal to the maximum value of X on the domain T. The research is concerned with the determination of the distributions of these functionals under various hypotheses about the probabilistic structure of X. It is assumed here that the random function is Gaussian or Markovian. Stochastic process, Extreme value, Sojourn time, Local time, Limiting distribution, Self- intersections of paths, Gaussian process, Markov process.
Publisher:
ISBN:
Category :
Languages : en
Pages : 2
Book Description
The subjects of this research are certain probabilistic properties of real and vector valued random functions X(t), where t is a generalized time parameter taking values in a subset T of Euclidean space. The distributions of three functionals of the random function X are studied. For any Borel set A in the range, the sojourn time of X in A is defined as the measure of the subset of the points t in T such that X(t) belongs to A. The self-intersection set of X is the subset of the set of points (s, t) in the product space of T such that s = t and X(s) = X(t). Finally, for a real valued random function X, the extreme value is the functional equal to the maximum value of X on the domain T. The research is concerned with the determination of the distributions of these functionals under various hypotheses about the probabilistic structure of X. It is assumed here that the random function is Gaussian or Markovian. Stochastic process, Extreme value, Sojourn time, Local time, Limiting distribution, Self- intersections of paths, Gaussian process, Markov process.
Research in Progress
Author:
Publisher:
ISBN:
Category : Military research
Languages : en
Pages : 274
Book Description
Publisher:
ISBN:
Category : Military research
Languages : en
Pages : 274
Book Description
Level Sets and Extrema of Random Processes and Fields
Author: Jean-Marc Azais
Publisher: John Wiley & Sons
ISBN: 0470434635
Category : Mathematics
Languages : en
Pages : 407
Book Description
A timely and comprehensive treatment of random field theory with applications across diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses how to understand the properties of the level sets of paths as well as how to compute the probability distribution of its extremal values, which are two general classes of problems that arise in the study of random processes and fields and in related applications. This book provides a unified and accessible approach to these two topics and their relationship to classical theory and Gaussian processes and fields, and the most modern research findings are also discussed. The authors begin with an introduction to the basic concepts of stochastic processes, including a modern review of Gaussian fields and their classical inequalities. Subsequent chapters are devoted to Rice formulas, regularity properties, and recent results on the tails of the distribution of the maximum. Finally, applications of random fields to various areas of mathematics are provided, specifically to systems of random equations and condition numbers of random matrices. Throughout the book, applications are illustrated from various areas of study such as statistics, genomics, and oceanography while other results are relevant to econometrics, engineering, and mathematical physics. The presented material is reinforced by end-of-chapter exercises that range in varying degrees of difficulty. Most fundamental topics are addressed in the book, and an extensive, up-to-date bibliography directs readers to existing literature for further study. Level Sets and Extrema of Random Processes and Fields is an excellent book for courses on probability theory, spatial statistics, Gaussian fields, and probabilistic methods in real computation at the upper-undergraduate and graduate levels. It is also a valuable reference for professionals in mathematics and applied fields such as statistics, engineering, econometrics, mathematical physics, and biology.
Publisher: John Wiley & Sons
ISBN: 0470434635
Category : Mathematics
Languages : en
Pages : 407
Book Description
A timely and comprehensive treatment of random field theory with applications across diverse areas of study Level Sets and Extrema of Random Processes and Fields discusses how to understand the properties of the level sets of paths as well as how to compute the probability distribution of its extremal values, which are two general classes of problems that arise in the study of random processes and fields and in related applications. This book provides a unified and accessible approach to these two topics and their relationship to classical theory and Gaussian processes and fields, and the most modern research findings are also discussed. The authors begin with an introduction to the basic concepts of stochastic processes, including a modern review of Gaussian fields and their classical inequalities. Subsequent chapters are devoted to Rice formulas, regularity properties, and recent results on the tails of the distribution of the maximum. Finally, applications of random fields to various areas of mathematics are provided, specifically to systems of random equations and condition numbers of random matrices. Throughout the book, applications are illustrated from various areas of study such as statistics, genomics, and oceanography while other results are relevant to econometrics, engineering, and mathematical physics. The presented material is reinforced by end-of-chapter exercises that range in varying degrees of difficulty. Most fundamental topics are addressed in the book, and an extensive, up-to-date bibliography directs readers to existing literature for further study. Level Sets and Extrema of Random Processes and Fields is an excellent book for courses on probability theory, spatial statistics, Gaussian fields, and probabilistic methods in real computation at the upper-undergraduate and graduate levels. It is also a valuable reference for professionals in mathematics and applied fields such as statistics, engineering, econometrics, mathematical physics, and biology.
Scientific and Technical Aerospace Reports
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1018
Book Description
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 1018
Book Description
Sojourns and Extremes of Stochastic Processes Ex. 2
Author: Simeon M. Berman
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages :
Book Description
Government Reports Annual Index
Author:
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 1200
Book Description
Publisher:
ISBN:
Category : Government publications
Languages : en
Pages : 1200
Book Description
Reports of the President and the Treasurer - John Simon Guggenheim Memorial Foundation
Author: John Simon Guggenheim Memorial Foundation
Publisher:
ISBN:
Category : Endowments
Languages : en
Pages : 778
Book Description
Includes: biographies of fellows appointed; reappointments; publications, musical compositions, academic appointments and index of fellows.
Publisher:
ISBN:
Category : Endowments
Languages : en
Pages : 778
Book Description
Includes: biographies of fellows appointed; reappointments; publications, musical compositions, academic appointments and index of fellows.
Bulletin - Institute of Mathematical Statistics
Author: Institute of Mathematical Statistics
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 994
Book Description
Publisher:
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 994
Book Description
Markov Processes, Gaussian Processes, and Local Times
Author: Michael B. Marcus
Publisher: Cambridge University Press
ISBN: 9780521863001
Category : Mathematics
Languages : en
Pages : 640
Book Description
A readable 2006 synthesis of three main areas in the modern theory of stochastic processes.
Publisher: Cambridge University Press
ISBN: 9780521863001
Category : Mathematics
Languages : en
Pages : 640
Book Description
A readable 2006 synthesis of three main areas in the modern theory of stochastic processes.
Reports of the President and of the Treasurer
Author: John Simon Guggenheim Memorial Foundation
Publisher:
ISBN:
Category : Research
Languages : en
Pages : 154
Book Description
Publisher:
ISBN:
Category : Research
Languages : en
Pages : 154
Book Description