Softcover ISBN:  9781470478391 
Product Code:  CLN/33 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
eBook ISBN:  9781470478681 
Product Code:  CLN/33.E 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
Softcover ISBN:  9781470478391 
eBook: ISBN:  9781470478681 
Product Code:  CLN/33.B 
List Price:  $118.00 $88.50 
MAA Member Price:  $106.20 $79.65 
AMS Member Price:  $94.40 $70.80 
Softcover ISBN:  9781470478391 
Product Code:  CLN/33 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
eBook ISBN:  9781470478681 
Product Code:  CLN/33.E 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
Softcover ISBN:  9781470478391 
eBook ISBN:  9781470478681 
Product Code:  CLN/33.B 
List Price:  $118.00 $88.50 
MAA Member Price:  $106.20 $79.65 
AMS Member Price:  $94.40 $70.80 

Book DetailsCourant Lecture NotesVolume: 33; 2024; Estimated: 244 ppMSC: Primary 60; 65
This textbook introduces the major ideas of stochastic analysis with a view to modeling or simulating systems involving randomness. Suitable for students and researchers in applied mathematics and related disciplines, this book prepares readers to solve concrete problems arising in physically motivated models. The author’s practical approach avoids measure theory while retaining rigor for cases where it helps build techniques or intuition.
Topics covered include Markov chains (discrete and continuous), Gaussian processes, Itô calculus, and stochastic differential equations and their associated PDEs. We ask questions such as: How does probability evolve? How do statistics evolve? How can we solve for timedependent quantities such as firstpassage times? How can we set up a model that includes fundamental principles such as timereversibility (detailed balance)? How can we simulate a stochastic process numerically?
Applied Stochastic Analysis invites readers to develop tools and insights for tackling physical systems involving randomness. Exercises accompany the text throughout, with frequent opportunities to implement simulation algorithms. A strong undergraduate background in linear algebra, probability, ODEs, and PDEs is assumed, along with the mathematical sophistication characteristic of a graduate student.
Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
ReadershipGraduate students and researchers interested in applied mathematics looking to use the ideas of stochastic analysis to model or simulate systems involving randomness.

Table of Contents

Introduction

Markov chains (I)

Markov chains (II): Detailed balance, and Markov chain Monte Carlo (MCMC)

Continuoustime Markov chains

Gaussian processes & stationary processes

Brownian motion

Stochastic integration

Stochastic differential equations

Numerically solvding SDEs

Forward and backward equations for SDEs

Some applicationis of the backward equation

Detailed balance, symmetry, and eigenfunction expansions

Asymptotic analysis of SDEs

Appendix

Bibliography

Index


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This textbook introduces the major ideas of stochastic analysis with a view to modeling or simulating systems involving randomness. Suitable for students and researchers in applied mathematics and related disciplines, this book prepares readers to solve concrete problems arising in physically motivated models. The author’s practical approach avoids measure theory while retaining rigor for cases where it helps build techniques or intuition.
Topics covered include Markov chains (discrete and continuous), Gaussian processes, Itô calculus, and stochastic differential equations and their associated PDEs. We ask questions such as: How does probability evolve? How do statistics evolve? How can we solve for timedependent quantities such as firstpassage times? How can we set up a model that includes fundamental principles such as timereversibility (detailed balance)? How can we simulate a stochastic process numerically?
Applied Stochastic Analysis invites readers to develop tools and insights for tackling physical systems involving randomness. Exercises accompany the text throughout, with frequent opportunities to implement simulation algorithms. A strong undergraduate background in linear algebra, probability, ODEs, and PDEs is assumed, along with the mathematical sophistication characteristic of a graduate student.
Titles in this series are copublished with the Courant Institute of Mathematical Sciences at New York University.
Graduate students and researchers interested in applied mathematics looking to use the ideas of stochastic analysis to model or simulate systems involving randomness.

Introduction

Markov chains (I)

Markov chains (II): Detailed balance, and Markov chain Monte Carlo (MCMC)

Continuoustime Markov chains

Gaussian processes & stationary processes

Brownian motion

Stochastic integration

Stochastic differential equations

Numerically solvding SDEs

Forward and backward equations for SDEs

Some applicationis of the backward equation

Detailed balance, symmetry, and eigenfunction expansions

Asymptotic analysis of SDEs

Appendix

Bibliography

Index