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Probabilistic solutions of the so called Schrödinger boundary data problem provide for a unique Markovian interpolation between any two strictly positive probability densities designed to form the input-output statistics data for the process taking place in a finite-time interval. The key issue is to select the jointly continuous in all variables positive… (More)

We combine earlier investigations of linear systems with Lévy fluc-We give a complete construction of the Ornstein-Uhlenbeck-Cauchy process as a fully computable model of an anomalous transport and a paradigm example of Doob's stable noise-supported Ornstein-Uhlenbeck process. Despite the nonexistence of all moments, we determine local characteristics… (More)

The main purpose of the paper is an essentially probabilistic analysis of relativistic quantum mechanics. It is based on the assumption that whenever probability distributions arise, there exists a stochastic process that is either responsible for temporal evolution of a given measure or preserves the measure in the stationary case. Our departure point is… (More)

- Ph Blanchard, A Jadczyk, R Olkiewicz
- 2001

Departing from classical concepts of ergodic theory, formulated in terms of probability densities, measures describing the chaotic behavior and the loss of information in quantum open systems are proposed. As application we discuss the chaotic outcomes of continuous measurement processes in the EEQT framework. Simultaneous measurement of four noncommuting… (More)

- R Olkiewicz
- 2000

A subclass of dynamical semigroups induced by the interaction of a quantum system with an environment is introduced. Such semigroups lead to the selection of a stable subalgebra of effective observables. The structure of this subalgebra is completely determined.

The existing formulations of the Schrödinger interpolating dynamics, which is constrained by the prescribed input-output statistics data, utilize strictly positive Feynman-Kac kernels. This implies that the related Markov diffusion processes admit vanishing probability densities only at the boundaries of the spatial volume confining the process. We extend… (More)

By departing from the previous attempt (Phys. Rev. E 51, 4114, (1995)) we give a detailed construction of conditional and perturbed Markov processes , under the assumption that the Cauchy law of probability replaces the Gaussian law (appropriate for the Wiener process) as the model of primordial noise. All considered processes are regarded as probabilistic… (More)

- Ph Blanchard, A Jadczyk, R Olkiewicz
- 1998

In the framework of event enhanced quantum theory (EEQT) a probabilistic construction of the piecewise deterministic process associated with a dynam-ical semigroup is presented. The process describes sample histories of individual systems and gives a unique algorithm generating time series of pointer readings in real experiments.

- Piotr Garbaczewski, Grzegorz Kondrat, Robert Olkiewicz
- 1997

We analyze the unforced and deterministically forced Burgers equation in the framework of the (diffusive) interpolating dynamics that solves the so-called Schrödinger boundary data problem for the random matter transport. This entails an exploration of the consistency conditions that allow to interpret dispersion of passive contaminants in the Burgers flow… (More)

- A Jadczyk, G Kondrat, R Olkiewicz
- 1997

We prove that, contrary to the standard quantum theory of continuous observation, in the formalism of Event Enhanced Quantum Theory the stochastic process generating sample histories of pairs (observed quantum system,observing classical apparatus)is unique. This result gives a rigorous basis to the previous heuristic argument of Blanchard and Jadczyk.