Author : Jean-Claude Falmagne
Publisher : McGraw-Hill Science, Engineering & Mathematics
Page : 296 pages
File Size : 50,62 MB
Release : 2002
Category : Mathematics
ISBN :
Designed for undergraduate mathematics students or graduate students in the sciences. This book can be used in a prerequisite course for Statistics (for math majors) or Mathematical Modeling. The first eighteen chapters could be used in a one-quarter course, and the entire text is suitable for a one-semester course.
Author : K. L. Chung
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 44,21 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 1475739737
This book provides an elementary introduction to probability theory and its applications. The emphasis is on essential probabilistic reasoning, amply motivated, explained and illustrated with a large number of carefully selected samples. The fourth edition adds material related to mathematical finance, as well as expansions on stable laws and martingales.
Author : Simon Tavaré
Publisher : Springer
Page : 320 pages
File Size : 18,1 MB
Release : 2004-01-30
Category : Mathematics
ISBN : 3540398740
This volume contains lectures given at the 31st Probability Summer School in Saint-Flour (July 8-25, 2001). Simon Tavaré’s lectures serve as an introduction to the coalescent, and to inference for ancestral processes in population genetics. The stochastic computation methods described include rejection methods, importance sampling, Markov chain Monte Carlo, and approximate Bayesian methods. Ofer Zeitouni’s course on "Random Walks in Random Environment" presents systematically the tools that have been introduced to study the model. A fairly complete description of available results in dimension 1 is given. For higher dimension, the basic techniques and a discussion of some of the available results are provided. The contribution also includes an updated annotated bibliography and suggestions for further reading. Olivier Catoni's course appears separately.
Author : Jeffrey S Rosenthal
Publisher : World Scientific
Page : 213 pages
File Size : 38,25 MB
Release : 2019-09-26
Category : Mathematics
ISBN : 9811207925
This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory.Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms.The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible.
Author : Oliver Knill
Publisher : World Scientific Publishing Company
Page : 500 pages
File Size : 26,65 MB
Release : 2017-01-31
Category : Mathematics
ISBN : 9789813109490
This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.
Author : K. L. Chung
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 49,54 MB
Release : 2013-03-09
Category : Mathematics
ISBN : 1475751141
In the past half-century the theory of probability has grown from a minor isolated theme into a broad and intensive discipline interacting with many other branches of mathematics. At the same time it is playing a central role in the mathematization of various applied sciences such as statistics, opera tions research, biology, economics and psychology-to name a few to which the prefix "mathematical" has so far been firmly attached. The coming-of-age of probability has been reflected in the change of contents of textbooks on the subject. In the old days most of these books showed a visible split personality torn between the combinatorial games of chance and the so-called "theory of errors" centering in the normal distribution. This period ended with the appearance of Feller's classic treatise (see [Feller l]t) in 1950, from the manuscript of which I gave my first substantial course in probability. With the passage of time probability theory and its applications have won a place in the college curriculum as a mathematical discipline essential to many fields of study. The elements of the theory are now given at different levels, sometimes even before calculus. The present textbook is intended for a course at about the sophomore level. It presupposes no prior acquaintance with the subject and the first three chapters can be read largely without the benefit of calculus.
Author : Kiyosi Ito
Publisher : Springer Science & Business Media
Page : 246 pages
File Size : 23,98 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 3662100657
This accessible introduction to the theory of stochastic processes emphasizes Levy processes and Markov processes. It gives a thorough treatment of the decomposition of paths of processes with independent increments (the Lévy-Itô decomposition). It also contains a detailed treatment of time-homogeneous Markov processes from the viewpoint of probability measures on path space. In addition, 70 exercises and their complete solutions are included.
Author : Hossein Pishro-Nik
Publisher :
Page : 746 pages
File Size : 29,38 MB
Release : 2014-08-15
Category : Probabilities
ISBN : 9780990637202
The book covers basic concepts such as random experiments, probability axioms, conditional probability, and counting methods, single and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalities; limit theorems and convergence; introduction to Bayesian and classical statistics; random processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion; simulation using MATLAB and R.
Author : Günter Last
Publisher : Cambridge University Press
Page : 315 pages
File Size : 32,88 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 : Henry C. Tuckwell
Publisher : Routledge
Page : 324 pages
File Size : 35,87 MB
Release : 2018-02-06
Category : Mathematics
ISBN : 1351452959
This book provides a clear and straightforward introduction to applications of probability theory with examples given in the biological sciences and engineering. The first chapter contains a summary of basic probability theory. Chapters two to five deal with random variables and their applications. Topics covered include geometric probability, estimation of animal and plant populations, reliability theory and computer simulation. Chapter six contains a lucid account of the convergence of sequences of random variables, with emphasis on the central limit theorem and the weak law of numbers. The next four chapters introduce random processes, including random walks and Markov chains illustrated by examples in population genetics and population growth. This edition also includes two chapters which introduce, in a manifestly readable fashion, the topic of stochastic differential equations and their applications.
