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Numerical Integration of Stochastic Differential Equations: 313 (Mathematics and Its Applications, 313) - Hardcover
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Synopsis
This book is devoted to mean-square and weak approximations of solutions of Stochastic Differential Equations (SDE). These approximations represent two fundamental aspects in the contemporary theory of SDE. Firstly, the construction of numerical methods for such systems is important as the solutions provided serve as characteristics for a number of mathematical physics problems. Secondly, the employment of probability representations together with a Monte Carlo method allows us to reduce the solution of complex multidimensional problems of mathematical physics to the integration of stochastic equations.Along with a general theory of numerical integrations of such systems, both in the mean-square and the weak sense, a number of concrete and sufficiently constructive numerical schemes are considered. Various applications and particularly the approximate calculation of Wiener integrals are also dealt with. This book is of interest to graduate students in the mathematical, physical and engineering sciences, and to specialists whose work involves differential equations, mathematical physics, numerical mathematics, the theory of random processes, estimation and control theory.
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- PublisherSpringer
- Publication date1994
- ISBN 10 079233213X
- ISBN 13 9780792332138
- BindingHardcover
- LanguageEnglish
- Number of pages180
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Numerical Integration of Stochastic Differential Equations (Mathematics and Its Applications).
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Numerical Integration of Stochastic Differential Equations
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Numerical Integration of Stochastic Differential Equations (Mathematics and Its Applications, 313)
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Numerical Integration of Stochastic Differential Equations (Mathematics and Its Applications, 313)
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Numerical Integration of Stochastic Differential Equations
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Springer Netherlands Nov 1994, 1994
ISBN 10: 079233213X
ISBN 13: 9780792332138
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -U sing stochastic differential equations we can successfully model systems that func tion in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochas tic differential equations lies, to a large extent, in the strong connections they have with the equations of mathematical physics. It is well known that problems in math ematical physics involve 'damned dimensions', of ten leading to severe difficulties in solving boundary value problems. A way out is provided by stochastic equations, the solutions of which of ten come about as characteristics. In its simplest form, the method of characteristics is as follows. Consider a system of n ordinary differential equations dX = a(X) dt. (O.l ) Let Xx(t) be the solution of this system satisfying the initial condition Xx(O) = x. For an arbitrary continuously differentiable function u(x) we then have: (0.2) u(Xx(t)) - u(x) = j (a(Xx(t)), ~~ (Xx(t))) dt. 184 pp. Englisch. Seller Inventory # 9780792332138
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Numerical Integration of Stochastic Differential Equations
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Introduction. 1: Mean-square approximation of solutions of systems of stochastic differential equations. 1. Theorem on the order of convergence (theorem on the relation between approximation on a finite interval and one-step approximation). 2. Methods . Seller Inventory # 5967292
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Numerical Integration of Stochastic Differential Equations
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Springer Netherlands, Springer Netherlands, 1994
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ISBN 13: 9780792332138
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Buch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - U sing stochastic differential equations we can successfully model systems that func tion in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochas tic differential equations lies, to a large extent, in the strong connections they have with the equations of mathematical physics. It is well known that problems in math ematical physics involve 'damned dimensions', of ten leading to severe difficulties in solving boundary value problems. A way out is provided by stochastic equations, the solutions of which of ten come about as characteristics. In its simplest form, the method of characteristics is as follows. Consider a system of n ordinary differential equations dX = a(X) dt. (O.l ) Let Xx(t) be the solution of this system satisfying the initial condition Xx(O) = x. For an arbitrary continuously differentiable function u(x) we then have: (0.2) u(Xx(t)) - u(x) = j (a(Xx(t)), ~~ (Xx(t))) dt. Seller Inventory # 9780792332138
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Numerical Integration of Stochastic Differential Equations
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Numerical Integration of Stochastic Differential Equations (Mathematics and Its Applications, 313)
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