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Kolmogorov Operators of Hamiltonian Systems Perturbed by Noise

  • Giuseppe Da Prato
  • Alessandra Lunardi
Part of the Operator Theory: Advances and Applications book series (OT, volume 168)

Abstract

We consider a second-order elliptic operator k arising from Hamiltonian systems with friction in ℝ2n perturbed by noise. An invariant measure for this operator is μ(dx, dy) = exp(−2H(x, y))dx dy, where H is the Hamiltonian. We study the realization K: H 2(ℝ2n , μ) ↦ L 2(ℝ2n , μ) of k in L 2(ℝ2n , μ), proving that it is m-dissipative and that it generates an analytic semigroup.

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Giuseppe Da Prato
    • 1
  • Alessandra Lunardi
    • 2
  1. 1.Scuola Normale SuperiorePisaItaly
  2. 2.Dipartimento di MatematicaUniversità di ParmaParmaItaly

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