Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations
We incorporate randomness into deterministic theories and compare analytically and numerically some well-known stochastic theories: the Liouville process, the Ornstein-Uhlenbeck process, and a process that is Gaussian and exponentially time correlated (Ornstein-Uhlenbeck noise). Different methods of...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2010-01-01
|
| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2010/509326 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567866150354944 |
|---|---|
| author | John F. Moxnes Kjell Hausken |
| author_facet | John F. Moxnes Kjell Hausken |
| author_sort | John F. Moxnes |
| collection | DOAJ |
| description | We incorporate randomness into deterministic theories and compare analytically and numerically some well-known stochastic theories: the Liouville process, the Ornstein-Uhlenbeck process, and a process that is Gaussian and exponentially time correlated (Ornstein-Uhlenbeck noise). Different methods of achieving the marginal densities for correlated and uncorrelated noise are discussed. Analytical results are presented for a deterministic linear friction force and a stochastic force that is uncorrelated or exponentially correlated. |
| format | Article |
| id | doaj-art-5f8e0839772340beaebfc28c428dda5f |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-5f8e0839772340beaebfc28c428dda5f2025-02-03T01:00:17ZengWileyAdvances in Mathematical Physics1687-91201687-91392010-01-01201010.1155/2010/509326509326Introducing Randomness into First-Order and Second-Order Deterministic Differential EquationsJohn F. Moxnes0Kjell Hausken1Department for Protection, Norwegian Defence Research Establishment, P.O. Box 25, 2007 Kjeller, NorwayFaculty of Social Sciences, University of Stavanger, 4036 Stavanger, NorwayWe incorporate randomness into deterministic theories and compare analytically and numerically some well-known stochastic theories: the Liouville process, the Ornstein-Uhlenbeck process, and a process that is Gaussian and exponentially time correlated (Ornstein-Uhlenbeck noise). Different methods of achieving the marginal densities for correlated and uncorrelated noise are discussed. Analytical results are presented for a deterministic linear friction force and a stochastic force that is uncorrelated or exponentially correlated.http://dx.doi.org/10.1155/2010/509326 |
| spellingShingle | John F. Moxnes Kjell Hausken Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations Advances in Mathematical Physics |
| title | Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations |
| title_full | Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations |
| title_fullStr | Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations |
| title_full_unstemmed | Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations |
| title_short | Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations |
| title_sort | introducing randomness into first order and second order deterministic differential equations |
| url | http://dx.doi.org/10.1155/2010/509326 |
| work_keys_str_mv | AT johnfmoxnes introducingrandomnessintofirstorderandsecondorderdeterministicdifferentialequations AT kjellhausken introducingrandomnessintofirstorderandsecondorderdeterministicdifferentialequations |