Kleden, P.E, Platen, E. Numerical solution of stochastic differential equations. The numerical solution of such equations is more complex than that of those only driven by Wiener processes, described in Kloeden & Platen: Numerical Solution of Stochastic Differential Equations … The stochastic Taylor expansion provides the basis for the discrete time numerical methods for differential equations. CYBER DEAL: 50% off all Springer eBooks | Get this offer! This book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasising the numerical methods needed to solve such equations. Not logged in In Itô calculus, the Euler–Maruyama method (also called the Euler method) is a method for the approximate numerical solution of a stochastic differential equation (SDE). The stochastic Taylor expansion provides the basis for the discrete time numerical methods for differential equations. Besides serving as a basic text on such methods, the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable. This chapter is an introduction and survey of numerical solution methods for stochastic differential equations. Stochastic differential equations (SDE) play an important role in a range of application areas, including biology, physics, chemistry, epidemiology, mechanics, microelectronics, economics, and finance . It assumes of the reader an undergraduate background in mathematical methods typical of engineers and physicists, though many chapters begin with a descriptive summary. Kloeden, Peter E., Platen, Eckhard. The book is also accessible to others who only require numerical recipes. Please review prior to ordering, ebooks can be used on all reading devices, Institutional customers should get in touch with their account manager, Usually ready to be dispatched within 3 to 5 business days, if in stock. Authors: (SMAP, volume 23), Over 10 million scientific documents at your fingertips. The book presents many new results on high-order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extra-polation and variance-reduction methods. The stochastic Taylor expansion provides the basis for the discrete time numerical methods for differential equations. This service is more advanced with JavaScript available, Part of the Springer, New York 1991 Springer, New York 1991 Google Scholar - (Applications of mathematics; 23) "Second corrected printing" - T. p. verso. Applications of Mathematics ISBN 3-540-54062-8 Springer-Verlag Berlin Heidelberg New Yor k ISBN 0-387-54062-8 Springer-Verlag New York Berlin Heidelber g Library of Congress Cataloging-in-Publication Data. price for Vietnam book series The book is also accessible to others who only require numerical recipes. The stochastic Taylor expansion provides the basis for the discrete time numerical methods for differential equations. The book presents many new results on high-order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extra-polation and variance-reduction methods. It is a simple generalization of the Euler method for ordinary differential equations to stochastic differential equations. ZAMP, Probability Theory and Stochastic Processes, Modelling with Stochastic Differential Equations, Applications of Stochastic Differential Equations, Time Discrete Approximation of Deterministic Differential Equations, Introduction to Stochastic Time Discrete Approximation, Selected Applications of Strong Approximations, Explicit and Implicit Weak Approximations, Selected Applications of Weak Approximations. Part of Springer Nature. Not affiliated JavaScript is currently disabled, this site works much better if you It is named after Leonhard Euler and Gisiro Maruyama. The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to peculiarities of stochastic calculus. The book presents many new results on high-order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extra-polation and variance-reduction methods. This was not an easy task... Their exposition stresses clarity, not formality - a very welcome approach." The solutions of SDEs are of a different character compared with the solutions of classical ordinary and partial differential equations in the sense that the solutions of SDEs are stochastic processes. It assumes of the reader an undergraduate background in mathematical methods typical of engineers and physicists, though many chapters begin with a descriptive summary. The numerical analysis of stochastic differential equations differs significantly from that of ordinary differential equations due to peculiarities of stochastic calculus. This book provides an introduction to stochastic calculus and stochastic differential equations, in both theory and applications, emphasising the numerical methods needed to solve such equations. ...you'll find more products in the shopping cart. To help the reader to develop an intuitive understanding of the underlying mathematics and hand-on numerical skills, exercises and over 100 PC-Exercises are included. Besides serving as a basic text on such methods, the book offers the reader ready access to a large number of potential research problems in a field that is just beginning to expand rapidly and is widely applicable. p. cm. © 2020 Springer Nature Switzerland AG. Springer is part of, Stochastic Modelling and Applied Probability, Please be advised Covid-19 shipping restrictions apply. The book presents many new results on high-order methods for strong sample path approximations and for weak functional approximations, including implicit, predictor-corrector, extra-polation and variance-reduction methods. (gross), © 2020 Springer Nature Switzerland AG. 185.207.228.65. Thus it is a nontrivial matter to measure the efficiency of a given algorithm for finding numerical solutions. enable JavaScript in your browser. "... 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. School of Mathematical Sciences and School of Finance & Economics, https://doi.org/10.1007/978-3-662-12616-5, Probability Theory and Stochastic Processes, Modelling with Stochastic Differential Equations, Applications of Stochastic Differential Equations, Time Discrete Approximation of Deterministic Differential Equations, Introduction to Stochastic Time Discrete Approximation, Selected Applications of Strong Approximations, Explicit and Implicit Weak Approximations, Selected Applications of Weak Approximations. To help the reader to develop an intuitive understanding of the underlying mathematics and hand-on numerical skills, exercises and over 100 PC-Exercises are included. Kloeden, Peter E. Numerical solution of stochastic differential equations/Peter E. Kloeden, Eckhard Platen.

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