Random Fields and Stochastic Partial Differential Equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1998
|
| Schriftenreihe: | Mathematics and Its Applications
438 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This book considers some models described by means of partial differential equations and boundary conditions with chaotic stochastic disturbance. In a framework of stochastic Partial Differential Equations an approach is suggested to generalize solutions of stochastic Boundary Problems. The main topic concerns probabilistic aspects with applications to well-known Random Fields models which are representative for the corresponding stochastic Sobolev spaces. (The term "stochastic" in general indicates involvement of appropriate random elements. ) It assumes certain knowledge in general Analysis and Probability (Hilbert space methods, Schwartz distributions, Fourier transform) . I A very general description of the main problems considered can be given as follows. Suppose, we are considering a random field ~ in a region T ~ Rd which is associated with a chaotic (stochastic) source"' by means of the differential equation (*) in T. A typical chaotic source can be represented by an appropriate random field"' with independent values, i. e. , generalized random function"' = ( cp, 'TJ), cp E C~(T), with independent random variables ( cp, 'fJ) for any test functions cp with disjoint supports. The property of having independent values implies a certain "roughness" of the random field "' which can only be treated functionally as a very irregular Schwarz distribution. With the lack of a proper development of nonlinear analyses for generalized functions, let us limit ourselves to the 1 For related material see, for example, J. L. Lions, E. |
| Beschreibung: | 1 Online-Ressource (VII, 232 p) |
| ISBN: | 9789401728386 9789048150090 |
| DOI: | 10.1007/978-94-017-2838-6 |
Internformat
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| 100 | 1 | |a Rozanov, Yu. A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Random Fields and Stochastic Partial Differential Equations |c by Yu. A. Rozanov |
| 264 | 1 | |a Dordrecht |b Springer Netherlands |c 1998 | |
| 300 | |a 1 Online-Ressource (VII, 232 p) | ||
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| 490 | 1 | |a Mathematics and Its Applications |v 438 | |
| 500 | |a This book considers some models described by means of partial differential equations and boundary conditions with chaotic stochastic disturbance. In a framework of stochastic Partial Differential Equations an approach is suggested to generalize solutions of stochastic Boundary Problems. The main topic concerns probabilistic aspects with applications to well-known Random Fields models which are representative for the corresponding stochastic Sobolev spaces. (The term "stochastic" in general indicates involvement of appropriate random elements. ) It assumes certain knowledge in general Analysis and Probability (Hilbert space methods, Schwartz distributions, Fourier transform) . I A very general description of the main problems considered can be given as follows. Suppose, we are considering a random field ~ in a region T ~ Rd which is associated with a chaotic (stochastic) source"' by means of the differential equation (*) in T. A typical chaotic source can be represented by an appropriate random field"' with independent values, i. e. , generalized random function"' = ( cp, 'TJ), cp E C~(T), with independent random variables ( cp, 'fJ) for any test functions cp with disjoint supports. The property of having independent values implies a certain "roughness" of the random field "' which can only be treated functionally as a very irregular Schwarz distribution. With the lack of a proper development of nonlinear analyses for generalized functions, let us limit ourselves to the 1 For related material see, for example, J. L. Lions, E. | ||
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Datensatz im Suchindex
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| author | Rozanov, Yu. A. |
| author_facet | Rozanov, Yu. A. |
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| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-017-2838-6 |
| format | Electronic eBook |
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| institution | BVB |
| isbn | 9789401728386 9789048150090 |
| language | English |
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| spelling | Rozanov, Yu. A. Verfasser aut Random Fields and Stochastic Partial Differential Equations by Yu. A. Rozanov Dordrecht Springer Netherlands 1998 1 Online-Ressource (VII, 232 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 438 This book considers some models described by means of partial differential equations and boundary conditions with chaotic stochastic disturbance. In a framework of stochastic Partial Differential Equations an approach is suggested to generalize solutions of stochastic Boundary Problems. The main topic concerns probabilistic aspects with applications to well-known Random Fields models which are representative for the corresponding stochastic Sobolev spaces. (The term "stochastic" in general indicates involvement of appropriate random elements. ) It assumes certain knowledge in general Analysis and Probability (Hilbert space methods, Schwartz distributions, Fourier transform) . I A very general description of the main problems considered can be given as follows. Suppose, we are considering a random field ~ in a region T ~ Rd which is associated with a chaotic (stochastic) source"' by means of the differential equation (*) in T. A typical chaotic source can be represented by an appropriate random field"' with independent values, i. e. , generalized random function"' = ( cp, 'TJ), cp E C~(T), with independent random variables ( cp, 'fJ) for any test functions cp with disjoint supports. The property of having independent values implies a certain "roughness" of the random field "' which can only be treated functionally as a very irregular Schwarz distribution. With the lack of a proper development of nonlinear analyses for generalized functions, let us limit ourselves to the 1 For related material see, for example, J. L. Lions, E. Mathematics Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Partial Differential Equations Mathematik Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 s Zufälliges Feld (DE-588)4191094-1 s 1\p DE-604 Mathematics and Its Applications 438 (DE-604)BV008163334 438 https://doi.org/10.1007/978-94-017-2838-6 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rozanov, Yu. A. Random Fields and Stochastic Partial Differential Equations Mathematics and Its Applications Mathematics Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Partial Differential Equations Mathematik Zufälliges Feld (DE-588)4191094-1 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| subject_GND | (DE-588)4191094-1 (DE-588)4135969-0 |
| title | Random Fields and Stochastic Partial Differential Equations |
| title_auth | Random Fields and Stochastic Partial Differential Equations |
| title_exact_search | Random Fields and Stochastic Partial Differential Equations |
| title_full | Random Fields and Stochastic Partial Differential Equations by Yu. A. Rozanov |
| title_fullStr | Random Fields and Stochastic Partial Differential Equations by Yu. A. Rozanov |
| title_full_unstemmed | Random Fields and Stochastic Partial Differential Equations by Yu. A. Rozanov |
| title_short | Random Fields and Stochastic Partial Differential Equations |
| title_sort | random fields and stochastic partial differential equations |
| topic | Mathematics Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Partial Differential Equations Mathematik Zufälliges Feld (DE-588)4191094-1 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| topic_facet | Mathematics Differential equations, partial Distribution (Probability theory) Probability Theory and Stochastic Processes Partial Differential Equations Mathematik Zufälliges Feld Stochastische partielle Differentialgleichung |
| url | https://doi.org/10.1007/978-94-017-2838-6 |
| volume_link | (DE-604)BV008163334 |
| work_keys_str_mv | AT rozanovyua randomfieldsandstochasticpartialdifferentialequations |