Markov processes and generalized Schrödinger equations
نویسنده
چکیده
Starting from the forward and backward infinitesimal generators of bilateral, timehomogeneous Markov processes, the self-adjoint Hamiltonians of the generalized Schrödinger equations are first introduced by means of suitable Doob transformations. Then, by broadening with the aid of the Dirichlet forms, the results of the Nelson stochastic mechanics, we prove that it is possible to associate bilateral, and timehomogeneous Markov processes to the wave functions stationary solutions of our generalized Schrödinger equations. Particular attention is then paid to the special case of the Lévy-Schrödinger (LS) equations and to their associated Lévy-type Markov processes, and to a few examples of Cauchy background noise. C © 2011 American Institute of Physics. [doi:10.1063/1.3663205]
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