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1999 An Extended Generator and Schrödinger Equations
Ronald Getoor
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Electron. J. Probab. 4: 1-23 (1999). DOI: 10.1214/EJP.v4-56


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.


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Ronald Getoor. "An Extended Generator and Schrödinger Equations." Electron. J. Probab. 4 1 - 23, 1999.


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

zbMATH: 0936.60066
MathSciNet: MR1741538
Digital Object Identifier: 10.1214/EJP.v4-56

Primary: 60J40
Secondary: 60J25 , 60J35 , 60J45

Keywords: generators , Markov processes , Schrödinger equations , smooth measures

Vol.4 • 1999
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