Introducing Randomness into First‐Order and Second‐Order Deterministic Differential Equations

John F. Moxnes and Kjell Hausken

Advances in Mathematical Physics, 2010, vol. 2010, issue 1

Abstract: 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.

Date: 2010
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https://doi.org/10.1155/2010/509326

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Journal Article: Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations (2010)
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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2010:y:2010:i:1:n:509326

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