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

John F. Moxnes and Kjell Hausken

Advances in Mathematical Physics, 2010, vol. 2010, 1-42

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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:509326

DOI: 10.1155/2010/509326

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