Institut C Jordan

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  Article: Markov chains approximation of jump-diffusion stochastic models in quantum measurement theory

  Institut C Jordan
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  ABSTRACT: The "Quantum trajectories" are solutions of stochastic differential equations also called Belavkin or stochastic Schrödinger equations. They describe random phe-nomenon in quantum measurement theory. Two type of such equations are classi-cally considered, one is driven by a one-dimensional brownian motion and the other is driven by a counting process. In this article, we present the way to obtain more advanced models which use jump-diffusion stochastic differential equations. Such models come from solutions of Martingale problems for infinitesimal generators. This generators are obtained from the limit of a concrete discrete model of discrete quantum trajectories which gives rise to classical Markov chains. Furthermore, the stochastic models of jump-diffusion equations is physically justified by proving that their solutions can be obtained as the limit of the discrete trajectories.
  12/2007;