MARC details
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04157nam a22004335i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
978-0-387-74317-2 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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| control field |
20250710084019.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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100301s2008 xxu| s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9780387743172 |
| -- |
99780387743172 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-0-387-74317-2 |
| Source of number or code |
doi |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
519.2 |
| Edition information |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Kotelenez, Peter. |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
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| Title |
Stochastic Ordinary and Stochastic Partial Differential Equations |
| Medium |
[recurso electrónico] : |
| Remainder of title |
Transition from Microscopic to Macroscopic Equations / |
| Statement of responsibility, etc. |
by Peter Kotelenez. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
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| Place of production, publication, distribution, manufacture |
New York, NY : |
| Name of producer, publisher, distributor, manufacturer |
Springer New York, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2008. |
| 300 ## - PHYSICAL DESCRIPTION |
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| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
recurso en línea |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Stochastic Modelling and Applied Probability formerly: Applications of Mathematics, |
| International Standard Serial Number |
0172-4568 ; |
| Volume/sequential designation |
58 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
From Microscopic Dynamics to Mesoscopic Kinematics -- Heuristics: Microscopic Model and Space-Time Scales -- Deterministic Dynamics in a Lattice Model and a Mesoscopic (Stochastic) Limit -- Proof of the Mesoscopic Limit Theorem -- Mesoscopic A: Stochastic Ordinary Differential Equations -- Stochastic Ordinary Differential Equations: Existence, Uniqueness, and Flows Properties -- Qualitative Behavior of Correlated Brownian Motions -- Proof of the Flow Property -- Comments on SODEs: A Comparison with Other Approaches -- Mesoscopic B: Stochastic Partial Differential Equations -- Stochastic Partial Differential Equations: Finite Mass and Extensions -- Stochastic Partial Differential Equations: Infinite Mass -- Stochastic Partial Differential Equations:Homogeneous and Isotropic Solutions -- Proof of Smoothness, Integrability, and Itô's Formula -- Proof of Uniqueness -- Comments on Other Approaches to SPDEs -- Macroscopic: Deterministic Partial Differential Equations -- Partial Differential Equations as a Macroscopic Limit -- General Appendix. |
| 520 ## - SUMMARY, ETC. |
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| Summary, etc. |
This book provides the first rigorous derivation of mesoscopic and macroscopic equations from a deterministic system of microscopic equations. The microscopic equations are cast in the form of a deterministic (Newtonian) system of coupled nonlinear oscillators for N large particles and infinitely many small particles. The mesoscopic equations are stochastic ordinary differential equations (SODEs) and stochastic partial differential equatuions (SPDEs), and the macroscopic limit is described by a parabolic partial differential equation. A detailed analysis of the SODEs and (quasi-linear) SPDEs is presented. Semi-linear (parabolic) SPDEs are represented as first order stochastic transport equations driven by Stratonovich differentials. The time evolution of correlated Brownian motions is shown to be consistent with the depletion phenomena experimentally observed in colloids. A covariance analysis of the random processes and random fields as well as a review section of various approaches to SPDEs are also provided. An extensive appendix makes the book accessible to both scientists and graduate students who may not be specialized in stochastic analysis. Probabilists, mathematical and theoretical physicists as well as mathematical biologists and their graduate students will find this book useful. Peter Kotelenez is a professor of mathematics at Case Western Reserve University in Cleveland, Ohio. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
MATHEMATICS. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
DISTRIBUTION (PROBABILITY THEORY). |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
MATHEMATICAL PHYSICS. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
MATHEMATICS. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
PROBABILITY THEORY AND STOCHASTIC PROCESSES. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
MATHEMATICAL METHODS IN PHYSICS. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Relationship information |
Printed edition: |
| International Standard Book Number |
9780387743165 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Stochastic Modelling and Applied Probability formerly: Applications of Mathematics, |
| International Standard Serial Number |
0172-4568 ; |
| Volume/sequential designation |
58 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
|---|
| Uniform Resource Identifier |
<a href="http://dx.doi.org/10.1007/978-0-387-74317-2">http://dx.doi.org/10.1007/978-0-387-74317-2</a> |
| Public note |
Ver el texto completo en las instalaciones del CICY |
| 912 ## - |
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| -- |
ZDB-2-SMA |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) |
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| Source of classification or shelving scheme |
Dewey Decimal Classification |
| Koha item type |
Libros electrónicos |
