Numerical Integration of Stochastic Differential Equations:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Dordrecht
Springer Netherlands
1995
|
| Series: | Mathematics and Its Applications
313 |
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | Using stochastic differential equations we can successfully model systems that function in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochastic 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 mathematical 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 |
| Physical Description: | 1 Online-Ressource (VIII, 172 p) |
| ISBN: | 9789401584555 9789048144877 |
| DOI: | 10.1007/978-94-015-8455-5 |
Staff View
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| 500 | |a Using stochastic differential equations we can successfully model systems that function in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochastic 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 mathematical 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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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-8455-5 |
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| isbn | 9789401584555 9789048144877 |
| language | English |
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| spelling | Milʹstejn, Grigorij N. 1937- Verfasser (DE-588)12144371X aut Numerical Integration of Stochastic Differential Equations by G. N. Milstein Dordrecht Springer Netherlands 1995 1 Online-Ressource (VIII, 172 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 313 Using stochastic differential equations we can successfully model systems that function in the presence of random perturbations. Such systems are among the basic objects of modern control theory. However, the very importance acquired by stochastic 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 mathematical 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 Computer science Electronic data processing Mathematics Distribution (Probability theory) Computer Science Numeric Computing Probability Theory and Stochastic Processes Applications of Mathematics Datenverarbeitung Informatik Mathematik Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Mathematics and Its Applications 313 (DE-604)BV008163334 313 https://doi.org/10.1007/978-94-015-8455-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Milʹstejn, Grigorij N. 1937- Numerical Integration of Stochastic Differential Equations Mathematics and Its Applications Computer science Electronic data processing Mathematics Distribution (Probability theory) Computer Science Numeric Computing Probability Theory and Stochastic Processes Applications of Mathematics Datenverarbeitung Informatik Mathematik Stochastische Differentialgleichung (DE-588)4057621-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4128130-5 |
| title | Numerical Integration of Stochastic Differential Equations |
| title_auth | Numerical Integration of Stochastic Differential Equations |
| title_exact_search | Numerical Integration of Stochastic Differential Equations |
| title_full | Numerical Integration of Stochastic Differential Equations by G. N. Milstein |
| title_fullStr | Numerical Integration of Stochastic Differential Equations by G. N. Milstein |
| title_full_unstemmed | Numerical Integration of Stochastic Differential Equations by G. N. Milstein |
| title_short | Numerical Integration of Stochastic Differential Equations |
| title_sort | numerical integration of stochastic differential equations |
| topic | Computer science Electronic data processing Mathematics Distribution (Probability theory) Computer Science Numeric Computing Probability Theory and Stochastic Processes Applications of Mathematics Datenverarbeitung Informatik Mathematik Stochastische Differentialgleichung (DE-588)4057621-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Computer science Electronic data processing Mathematics Distribution (Probability theory) Computer Science Numeric Computing Probability Theory and Stochastic Processes Applications of Mathematics Datenverarbeitung Informatik Mathematik Stochastische Differentialgleichung Numerisches Verfahren |
| url | https://doi.org/10.1007/978-94-015-8455-5 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT milʹstejngrigorijn numericalintegrationofstochasticdifferentialequations |