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Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson case
In quantum physics, recent investigations deal with the so-called "quantum
trajectory" theory. Heuristic rules are usually used to give rise to
"stochastic Schrodinger equations" which are stochastic differential equations
of non-usual type describing the physical models. These equations pose tedious
problems in terms of mathematical justification: notion of solution, existence,
uniqueness, justification... In this article, we concentrate on a particular
case: the Poisson case. Random measure theory is used in order to give rigorous
sense to such equations. We prove existence and uniqueness of a solution for
the associated stochastic equation. Furthermore, the stochastic model is
physically justified by proving that the solution can be obtained as a limit of
a concrete discrete time physical model.Comment: 35 page
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