Author : Martin Jacobsen
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 15,58 MB
Release : 2006-07-27
Category : Mathematics
ISBN : 0817644636
Mathematically rigorous exposition of the basic theory of marked point processes and piecewise deterministic stochastic processes Point processes are constructed from scratch with detailed proofs Includes applications with examples and exercises in survival analysis, branching processes, ruin probabilities, sports (soccer), finance and risk management, and queueing theory Accessible to a wider cross-disciplinary audience
Author : D.J. Daley
Publisher : Springer Science & Business Media
Page : 487 pages
File Size : 45,86 MB
Release : 2006-04-10
Category : Mathematics
ISBN : 0387215646
Point processes and random measures find wide applicability in telecommunications, earthquakes, image analysis, spatial point patterns, and stereology, to name but a few areas. The authors have made a major reshaping of their work in their first edition of 1988 and now present their Introduction to the Theory of Point Processes in two volumes with sub-titles Elementary Theory and Models and General Theory and Structure. Volume One contains the introductory chapters from the first edition, together with an informal treatment of some of the later material intended to make it more accessible to readers primarily interested in models and applications. The main new material in this volume relates to marked point processes and to processes evolving in time, where the conditional intensity methodology provides a basis for model building, inference, and prediction. There are abundant examples whose purpose is both didactic and to illustrate further applications of the ideas and models that are the main substance of the text.
Author : Georg Lindgren
Publisher : CRC Press
Page : 378 pages
File Size : 19,30 MB
Release : 2012-10-01
Category : Mathematics
ISBN : 1466557796
Intended for a second course in stationary processes, Stationary Stochastic Processes: Theory and Applications presents the theory behind the field’s widely scattered applications in engineering and science. In addition, it reviews sample function properties and spectral representations for stationary processes and fields, including a portion on stationary point processes. Features Presents and illustrates the fundamental correlation and spectral methods for stochastic processes and random fields Explains how the basic theory is used in special applications like detection theory and signal processing, spatial statistics, and reliability Motivates mathematical theory from a statistical model-building viewpoint Introduces a selection of special topics, including extreme value theory, filter theory, long-range dependence, and point processes Provides more than 100 exercises with hints to solutions and selected full solutions This book covers key topics such as ergodicity, crossing problems, and extremes, and opens the doors to a selection of special topics, like extreme value theory, filter theory, long-range dependence, and point processes, and includes many exercises and examples to illustrate the theory. Precise in mathematical details without being pedantic, Stationary Stochastic Processes: Theory and Applications is for the student with some experience with stochastic processes and a desire for deeper understanding without getting bogged down in abstract mathematics.
Author : Tomas Björk
Publisher : Cambridge University Press
Page : 323 pages
File Size : 23,34 MB
Release : 2021-06-17
Category : Business & Economics
ISBN : 1316518671
Develop a deep understanding and working knowledge of point-process theory as well as its applications in finance.
Author : Sidney I. Resnick
Publisher : Springer
Page : 334 pages
File Size : 12,5 MB
Release : 2013-12-20
Category : Mathematics
ISBN : 0387759530
This book examines the fundamental mathematical and stochastic process techniques needed to study the behavior of extreme values of phenomena based on independent and identically distributed random variables and vectors. It emphasizes the core primacy of three topics necessary for understanding extremes: the analytical theory of regularly varying functions; the probabilistic theory of point processes and random measures; and the link to asymptotic distribution approximations provided by the theory of weak convergence of probability measures in metric spaces.
Author : Günter Last
Publisher : Cambridge University Press
Page : 315 pages
File Size : 14,98 MB
Release : 2017-10-26
Category : Mathematics
ISBN : 1107088011
A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Author : Günter Last
Publisher : Springer Science & Business Media
Page : 522 pages
File Size : 14,49 MB
Release : 1995-08-10
Category : Mathematics
ISBN : 9780387945477
This book gives a self-contained introduction to the dynamic martingale approach to marked point processes (MPP). Based on the notion of a compensator, this approach gives a versatile tool for analyzing and describing the stochastic properties of an MPP. In particular, the authors discuss the relationship of an MPP to its compensator and particular classes of MPP are studied in great detail. The theory is applied to study properties of dependent marking and thinning, to prove results on absolute continuity of point process distributions, to establish sufficient conditions for stochastic ordering between point and jump processes, and to solve the filtering problem for certain classes of MPPs.
Author : Adrian Baddeley
Publisher : CRC Press
Page : 830 pages
File Size : 19,40 MB
Release : 2015-11-11
Category : Mathematics
ISBN : 1482210215
Modern Statistical Methodology and Software for Analyzing Spatial Point PatternsSpatial Point Patterns: Methodology and Applications with R shows scientific researchers and applied statisticians from a wide range of fields how to analyze their spatial point pattern data. Making the techniques accessible to non-mathematicians, the authors draw on th
Author : M.N.M. van Lieshout
Publisher : CRC Press
Page : 221 pages
File Size : 46,1 MB
Release : 2019-03-19
Category : Mathematics
ISBN : 0429627033
Theory of Spatial Statistics: A Concise Introduction presents the most important models used in spatial statistics, including random fields and point processes, from a rigorous mathematical point of view and shows how to carry out statistical inference. It contains full proofs, real-life examples and theoretical exercises. Solutions to the latter are available in an appendix. Assuming maturity in probability and statistics, these concise lecture notes are self-contained and cover enough material for a semester course. They may also serve as a reference book for researchers. Features * Presents the mathematical foundations of spatial statistics. * Contains worked examples from mining, disease mapping, forestry, soil and environmental science, and criminology. * Gives pointers to the literature to facilitate further study. * Provides example code in R to encourage the student to experiment. * Offers exercises and their solutions to test and deepen understanding. The book is suitable for postgraduate and advanced undergraduate students in mathematics and statistics.
Author : David Pollard
Publisher : IMS
Page : 100 pages
File Size : 49,73 MB
Release : 1990
Category : Distribution (Probability theory).
ISBN : 9780940600164
