Electronic Journal of Probability

An Extended Generator and Schrödinger Equations

Ronald Getoor

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The generator of a Borel right processis extended so that it maps functions to smooth measures. This extension may be defined either probabilistically using martingales or analytically in terms of certain kernels on the state space of the process. Then the associated Schrödinger equation with a (signed) measure serving as potential may be interpreted as an equation between measures. In this context general existence and uniqueness theorems for solutions are established. These are then specialized to obtain more concrete results in special situations.

Article information

Electron. J. Probab., Volume 4 (1999), paper no. 19, 23 pp.

Accepted: 16 November 1999
First available in Project Euclid: 4 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J40: Right processes
Secondary: 60J25: Continuous-time Markov processes on general state spaces 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

Markov processes Schrödinger equations generators smooth measures

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Getoor, Ronald. An Extended Generator and Schrödinger Equations. Electron. J. Probab. 4 (1999), paper no. 19, 23 pp. doi:10.1214/EJP.v4-56. https://projecteuclid.org/euclid.ejp/1457125528

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