Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients write by Martin Hutzenthaler. This book was released on 2015-06-26. Numerical Approximations of Stochastic Differential Equations with Non-Globally Lipschitz Continuous Coefficients available in PDF, EPUB and Kindle. Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method diverge for these SDEs in finite time. This article develops a general theory based on rare events for studying integrability properties such as moment bounds for discrete-time stochastic processes. Using this approach, the authors establish moment bounds for fully and partially drift-implicit Euler methods and for a class of new explicit approximation methods which require only a few more arithmetical operations than the Euler-Maruyama method. These moment bounds are then used to prove strong convergence of the proposed schemes. Finally, the authors illustrate their results for several SDEs from finance, physics, biology and chemistry.
Stochastic Differential Equations with Markovian Switching
Stochastic Differential Equations with Markovian Switching - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Stochastic Differential Equations with Markovian Switching write by Xuerong Mao. This book was released on 2006. Stochastic Differential Equations with Markovian Switching available in PDF, EPUB and Kindle. This textbook provides the first systematic presentation of the theory of stochastic differential equations with Markovian switching. It presents the basic principles at an introductory level but emphasizes current advanced level research trends. The material takes into account all the features of Ito equations, Markovian switching, interval systems and time-lag. The theory developed is applicable in different and complicated situations in many branches of science and industry.
Numerical Solution of Stochastic Differential Equations
Numerical Solution of Stochastic Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Numerical Solution of Stochastic Differential Equations write by Peter E. Kloeden. This book was released on 2013-04-17. Numerical Solution of Stochastic Differential Equations available in PDF, EPUB and Kindle. The numerical analysis of stochastic differential equations (SDEs) differs significantly from that of ordinary differential equations. This book provides an easily accessible introduction to SDEs, their applications and the numerical methods to solve such equations. From the reviews: "The authors draw upon their own research and experiences in obviously many disciplines... considerable time has obviously been spent writing this in the simplest language possible." --ZAMP
Monte Carlo and Quasi-Monte Carlo Methods
Monte Carlo and Quasi-Monte Carlo Methods - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Monte Carlo and Quasi-Monte Carlo Methods write by Art B. Owen. This book was released on 2018-07-03. Monte Carlo and Quasi-Monte Carlo Methods available in PDF, EPUB and Kindle. This book presents the refereed proceedings of the Twelfth International Conference on Monte Carlo and Quasi-Monte Carlo Methods in Scientific Computing that was held at Stanford University (California) in August 2016. These biennial conferences are major events for Monte Carlo and quasi-Monte Carlo researchers. The proceedings include articles based on invited lectures as well as carefully selected contributed papers on all theoretical aspects and applications of Monte Carlo and quasi-Monte Carlo methods. Offering information on the latest developments in these very active areas, this book is an excellent reference resource for theoreticians and practitioners interested in solving high-dimensional computational problems, arising in particular, in finance, statistics, computer graphics and the solution of PDEs.
Exact Finite-Difference Schemes
Exact Finite-Difference Schemes - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Exact Finite-Difference Schemes write by Sergey Lemeshevsky. This book was released on 2016-09-26. Exact Finite-Difference Schemes available in PDF, EPUB and Kindle. Exact Finite-Difference Schemes is a first overview of the topic also describing the state-of-the-art in this field of numerical analysis. Construction of exact difference schemes for various parabolic and elliptic partial differential equations are discussed, including vibrations and transport problems. After this, applications are discussed, such as the discretisation of ODEs and PDEs and numerical methods for stochastic differential equations. Contents: Basic notation Preliminary results Hyperbolic equations Parabolic equations Use of exact difference schemes to construct NSFD discretizations of differential equations Exact and truncated difference schemes for boundary-value problem Exact difference schemes for stochastic differential equations Numerical blow-up time Bibliography
