2011/07/31 by Andrea Andrisani, Nicola Cufaro Petroni
Mathematics · Physics and Astronomy · #Dirichlet distribution #Infinitesimal #Markov chain #Markov kernel #Markov model #Markov process #Markov property #Markov renewal process #Quantum Mechanics and Applications #Spectral Theory in Mathematical Physics #cond-mat.stat-mech #math.PR #msc:47D07 #msc:60G51 #msc:60J35 #quant-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.1063/1.3663205
published as J. Math. Phys. 52 (2011) 113509 · 33 pages, 2 figures; corrected as required by referee; references added; in press on J. Math. Phys
openalex publication_date 2011/11/01 · arxiv created 2011/11/16 · arxiv updated 2014/09/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Starting from the forward and backward infinitesimal generators of bilateral, time-homogeneous 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 time-homogeneous 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.