Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients ( Memoirs of the American Mathematical Society )

Publication series ：Memoirs of the American Mathematical Society

Author： Martin Hutzenthaler;Arnulf Jentzen

Publisher： American Mathematical Society‎

Publication year： 2015

E-ISBN: 9781470422783

P-ISBN(Paperback): 9781470409845

Subject： O211.63 Stochastic Differential Equations

Keyword： Analysis

Language： ENG

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Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients

Chapter

Cover

Title page

Chapter 1. Introduction

1.1. Notation

Chapter 2. Integrability properties of approximation processes for SDEs

2.1. General discrete-time stochastic processes

2.2. Explicit approximation schemes

2.3. Implicit approximation schemes

Chapter 3. Convergence properties of approximation processes for SDEs

3.1. Setting and assumptions

3.2. Consistency

3.3. Convergence in probability

3.4. Strong convergence

3.5. Weak convergence

3.6. Numerical schemes for SDEs

Chapter 4. Examples of SDEs

4.1. Setting and assumptions

4.2. Stochastic van der Pol oscillator

4.3. Stochastic Duffing-van der Pol oscillator

4.4. Stochastic Lorenz equation

4.5. Stochastic Brusselator in the well-stirred case

4.6. Stochastic SIR model

4.7. Experimental psychology model

4.8. Scalar stochastic Ginzburg-Landau equation

4.9. Stochastic Lotka-Volterra equations

4.10. Volatility processes

4.11. Overdamped Langevin equation

Bibliography

Back Cover

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