Abstract
As part of a program to evaluate expectations in complex distributions by longterm averages of solutions to Langevin equations with complex dirft, a simple one-dimensional example is examined in some detail. The validity and rate of convergence of this scheme depends on the spectrum of an associated non-selfadjoint Hamiltonian which is found numerically. In the regime where the stochastic evaluation should be accurate numerical solution of the Langevin equation shows this to be the case.
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Klauder, J.R., Petersen, W.P. Spectrum of certain non-self-adjoint operators and solutions of Langevin equations with complex drift. J Stat Phys 39, 53–72 (1985). https://doi.org/10.1007/BF01007974
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DOI: https://doi.org/10.1007/BF01007974