Kolmogorov Operators of Hamiltonian Systems Perturbed by Noise
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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