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

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  • John F. Moxnes
  • Kjell Hausken

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.

Suggested Citation

  • John F. Moxnes & Kjell Hausken, 2010. "Introducing Randomness into First‐Order and Second‐Order Deterministic Differential Equations," Advances in Mathematical Physics, John Wiley & Sons, vol. 2010(1).
    • Handle: RePEc:wly:jnlamp:v:2010:y:2010:i:1:n:509326
    DOI: 10.1155/2010/509326
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    1. Czopnik, Radosław & Garbaczewski, Piotr, 2003. "Frictionless random dynamics: hydrodynamical formalism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 317(3), pages 449-471.
    2. Martin Rypdal & Kristoffer Rypdal, 2007. "A stochastic theory for temporal fluctuations in self-organized critical systems," Papers 0710.4010, arXiv.org, revised Jul 2008.
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