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Numerical Integration of Stochastic Differential Equations (Mathematics and Its Applications, 313) - Hardcover
Synopsis
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.
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Language Notes
Text: English (translation)
Original Language: Russian
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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
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Springer Netherlands Nov 1994, 1994
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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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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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