Weak Markov processes as linear systems

  title={Weak Markov processes as linear systems},
  author={Rolf Gohm},
  journal={Mathematics of Control, Signals, and Systems},
  • R. Gohm
  • Published 2 June 2012
  • Mathematics
  • Mathematics of Control, Signals, and Systems
A noncommutative Fornasini–Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter the resulting structure is worked out systematically and some quantum mechanical interpretations are given. We introduce subprocesses and quotient processes and then the notion of a $$\gamma $$γ-extension for processes which leads to a complete classification of all the ways in which processes can… 
1 Citations
Universal Preparability of States and Asymptotic Completeness
We introduce a notion of universal preparability for a state of a system, more precisely: for a normal state on a von Neumann algebra. It describes a situation where from an arbitrary initial state


Conservative Structured Noncommutative Multidimensional Linear Systems
We introduce a class of conservative structured multidimensional linear systems with evolution along a free semigroup. The system matrix for such a system is unitary and the associated transfer
Structured Noncommutative Multidimensional Linear Systems
Standard system-theoretic properties are developed for a class of multidimensional linear systems with evolution along a free semigroup and the connections with the much earlier studied theory of rational and recognizable formal power series are drawn.
Equivalence Classes and Local Asymptotic Normality in System Identification for Quantum Markov Chains
We consider the problem of identifying and estimating dynamical parameters of an ergodic quantum Markov chain, when only the stationary output is accessible for measurements. The starting point of
Quantum Feedback Networks: Hamiltonian Formulation
The model is non-Markovian for finite time delays, but in the limit where these delays vanish the model is recovered a Markov model and the rules for introducing feedback into arbitrary quantum networks are deduced.
Scattering Systems with Several Evolutions and Multidimensional Input/State/Output Systems
Abstract.The one-to-one correspondence between one-dimensional linear (stationary, causal) input/state/output systems and scattering systems with one evolution operator, in which the scattering
Isometric dilations for infinite sequences of noncommuting operators
This paper develops a dilation theory for {T,}n=l an infinite sequence of noncommuting operators on a Hilbert space, when the matrix [T1, T2, ... ] is a contraction. A Wold decomposition for an
Stochastic Schrödinger Equations as Limit of Discrete Filtering
It is shown that, starting from the correponding limiting open systems dynamics, the theory of quantum filtering leads to the same equations, therefore establishing consistency of the quantum stochastic approach for limiting Markovian models.
The fundamental mathematical de…nitions of the controlled Markov dynamics of quantum-mechanical systems are formulated with regard for the statistical reduction of quantum states in the course of
De Branges-Rovnyak Operator Models and Systems Theory: A Survey
We arrive at the de Branges-Rovnyak space D(W) from the point of view of model theory, i. e., as the space associated with a canonical model for a general completely nonunitary contraction operator
Generalized repeated interaction model and transfer functions
Using a scheme involving a lifting of a row contraction we introduce a toy model of repeated interactions between quantum systems. In this model there is an outgoing Cuntz scattering system involving