The Annals of Applied Probability

Basic properties of nonlinear stochastic Schrödinger equations driven by Brownian motions

Carlos M. Mora and Rolando Rebolledo

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The paper is devoted to the study of nonlinear stochastic Schrödinger equations driven by standard cylindrical Brownian motions (NSSEs) arising from the unraveling of quantum master equations. Under the Born–Markov approximations, this class of stochastic evolutions equations on Hilbert spaces provides characterizations of both continuous quantum measurement processes and the evolution of quantum systems. First, we deal with the existence and uniqueness of regular solutions to NSSEs. Second, we provide two general criteria for the existence of regular invariant measures for NSSEs. We apply our results to a forced and damped quantum oscillator.

Article information

Ann. Appl. Probab., Volume 18, Number 2 (2008), 591-619.

First available in Project Euclid: 20 March 2008

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Zentralblatt MATH identifier

Primary: 60H15: Stochastic partial differential equations [See also 35R60]
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 37L40: Invariant measures 81S25: Quantum stochastic calculus 81P15: Quantum measurement theory

Nonlinear stochastic Schrödinger equations regular invariant measures existence and uniqueness of solutions quantum mechanics stochastic evolution equations


Mora, Carlos M.; Rebolledo, Rolando. Basic properties of nonlinear stochastic Schrödinger equations driven by Brownian motions. Ann. Appl. Probab. 18 (2008), no. 2, 591--619. doi:10.1214/105051607000000311.

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