An Extended Generator and Schrödinger Equations
Ronald K. Getoor, University of California, San Diego
Abstract
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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