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Lagrangian dynamics for a passive tracer in a class of Gaussian Markovian flows

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  • Fannjiang, Albert
  • Komorowski, Tomasz
  • Peszat, Szymon

Abstract

We formulate a stochastic differential equation describing the Lagrangian environment process of a passive tracer in Ornstein-Uhlenbeck velocity fields. We subsequently prove a local existence and uniqueness result when the velocity field is regular. When the Ornstein-Uhlenbeck velocity field is only spatially Hölder continuous we construct and identify the probability law for the Lagranging process under a condition on the time correlation function and the Hölder exponent.

Suggested Citation

  • Fannjiang, Albert & Komorowski, Tomasz & Peszat, Szymon, 2002. "Lagrangian dynamics for a passive tracer in a class of Gaussian Markovian flows," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 171-198, February.
    • Handle: RePEc:eee:spapps:v:97:y:2002:i:2:p:171-198
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    References listed on IDEAS

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    1. Peszat, Szymon & Zabczyk, Jerzy, 1997. "Stochastic evolution equations with a spatially homogeneous Wiener process," Stochastic Processes and their Applications, Elsevier, vol. 72(2), pages 187-204, December.
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    1. Komorowski, Tomasz & Olla, Stefano, 2003. "Invariant measures for passive tracer dynamics in Ornstein-Uhlenbeck flows," Stochastic Processes and their Applications, Elsevier, vol. 105(1), pages 139-173, May.

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