Introducing randomness into first-order and second-order deterministic differential equations (Q606157)
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scientific article; zbMATH DE number 5816372
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Introducing randomness into first-order and second-order deterministic differential equations |
scientific article; zbMATH DE number 5816372 |
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Introducing randomness into first-order and second-order deterministic differential equations (English)
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16 November 2010
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Summary: 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.
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Liouville process
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Ornstein-Uhlenbeck process
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deterministic linear friction force
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stochastic force
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