arXiv subjects

Ricardo Castro Santis

Publications and source records attributed to Ricardo Castro Santis.

3 recordsLinked to original sources

arXiv2015

Stopping Time and Control for a Type of Impulsive Stochastic Differential Equation

The main objective of this paper is the construction of the solution of an impulsive stochastic differential equation, subject to control conditions in the pulse-times and give sufficient conditions for them to be random variables with finite expectation. Such equations are useful in modeling diverse phenomena as biological control and pressure regulating mechanisms. The article ends with an application in fishery.

math.PR↗

arXiv2014

Quantum Stochastic Dynamics in Multi-Photon Optics

In this work a generic model of \emph{multi-photon optics} is studied. It is considered $m$ pump and $n$ subharmonic fields. It shows how the multi-photon system, with direct and homodyne detection, can be obtained rigorously in the context of \emph{Measurement theory in Open Quantum System} (see \cite{Bar-OQS}, \cite{Bar-1990-QO} and \cite{RCS-LAP}). This is done trough the \emph{Quantum Stochastic Differential Equations} with unbounded coefficients (see \cite{Fagnola-Wills}, and \cite{RCS-LAP}). In particular the existence of the dynamics is proved, and a continuous measurements scheme is provided.

math.PR↗

arXiv2010

Quantum stochastic differential equations and continuous measurements: unbounded coefficients

A natural formulation of the theory of quantum measurements in continuous time is based on quantum stochastic differential equations (Hudson-Parthasarathy equations). However, such a theory was developed only in the case of Hudson-Parthasarathy equations with bounded coefficients. By using some results on Hudson-Parthasarathy equations with unbounded coefficients, we are able to extend the theory of quantum continuous measurements to cases in which unbounded operators on the system space are involved. A significant example of a quantum optical system (the degenerate parametric oscillator) is shown to fulfill the hypotheses introduced in the general theory.

math.PR↗