Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations
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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.
Moxnes, John Fredrik; Hausken, Kjell. Introducing Randomness into First-Order and Second-Order Deterministic Differential Equations. Advances in Mathematical Physics 2010 s. -