Numerical integration of stochastic differential equations /
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| Author / Creator: | Milʹshteĭn, G. N. (Grigoriĭ Noĭkhovich). |
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| Uniform title: | Chislennoe integrirovanie stokhasticheskikh different͡sialʹnykh uravneniĭ. English |
| Imprint: | Dordrecht ; Boston : Kluwer Academic Publishers, c1995. |
| Description: | vii, 169 p. ; 25 cm. |
| Language: | English |
| Series: | Mathematics and its applications ; v. 313 Mathematics and its applications (Kluwer Academic Publishers) ; v. 313. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/1763573 |
| Summary: | 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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| Physical Description: | vii, 169 p. ; 25 cm. |
| Bibliography: | Includes bibliographical references (p. 165-168) and index. |
| ISBN: | 079233213X |
