On Stochastic Generators of Positive Definite Exponents

Details On Stochastic Generators of Positive Definite Exponents On Stochastic Generators of Positive Definite Exponents

2005-12-13

arxiv.org/abs/math/0512290v1

Published in: Transactions of a Japanese-German Symposium Infinite Dimensional Harmonic Analysis 84--92, Eds: H. Heyer et al,

Mathematics

Probability

9 pages. Paper for Japanese-German Symposium `Infinite Dimensional Harmonic Analysis', Kyoto, 2000

Scientific paper

A characterisation of quantum stochastic positive definite (PD) exponent is given in terms of the conditional positive definiteness (CPD) of their form-generator. The pseudo-Hilbert dilation of the stochastic form-generator and the pre-Hilbert dilation of the corresponding dissipator is found. The structure of quasi-Poisson stochastic generators giving rise to a quantum stochastic birth processes is studied.

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