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Stability of piecewise-deterministic Markov processes

Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 1999
Summary: We study a form of stability for a general family of nondiffusion Markov processes known in the literature as piecewise-deterministic Markov processes (PDMP). By stability here we mean the existence of an invariant probability measure for the PDMP.
Dufour, François, Costa, Oswaldo L. V.
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Stability and Ergodicity of Piecewise Deterministic Markov Processes

SIAM Journal on Control and Optimization, 2008
The main goal of this paper is to establish some equivalence results on stability, recurrence, and ergodicity between a piecewise deterministic Markov process (PDMP) $\{X(t)\}$ and an embedded discrete-time Markov chain $\{\Theta_{n}\}$ generated by a Markov kernel $G$ that can be explicitly characterized in terms of the three local characteristics of ...
Oswaldo L. V. Costa, François Dufour
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On the Poisson Equation for Piecewise-Deterministic Markov Processes

SIAM Journal on Control and Optimization, 2003
Summary: We study the problem of the existence of a solution for the Poisson equation (PE) associated to a piecewise-deterministic Markov process (PDP). It is well known that the long run average cost of a stochastic process can be obtained through a solution of the PE associated with the process.
Oswaldo L. V. Costa, François Dufour
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Deterministic buffer synchronization of sequential processes

Acta Informatica, 1982
Co-operation of sequential processes is one of the most widely known organization principles for distributed systems. We shall consider the class of those systems of sequential processes which communicate deterministically by means of buffers and discuss proof rules to decide whether or not deadlocks can occur in a given system of this type.
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A Modal Logic for Non-Deterministic Discourse Processing

Journal of Logic, Language and Information, 1999
Inspired by context-dependence of interpreting an arbitrary English sentence, the author develops a Kripkean modal logic \({\mathcal L}_0\) that makes it possible to treat statements of the form \[ \text{` ``}e\text{ may'' translate to a logical form entailing }\varphi \text{'} \] as modal formulas.
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Markov Decision Processes and Deterministic Büchi Automata

Fundamenta Informaticae, 2002
We prove that given a Markov Decision Process (MDP) and a fixed subset of its states~F, there is a Markov policy which maximizes everywhere the probability to reach F infinitely often. Moreover such a maximum policy is computable in polytime in the size of the MDP.
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Real-valued Deterministic Processes

2015
In science, one-dimensional deterministic (i.e., non-random) systems provide the simplest models for processes that evolve over time. Mathematically, these models take the form of one-dimensional difference or differential equations. This chapter presents the basic theory of Benford's law for them.
Arno Berger, Theodore P. Hill
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Deterministically Timed Process Algebra

2009
Concurrent and distributed systems are characterized not only by their functional behavior, but also by their quantitative features. A prominent role is played by timing aspects, which express the temporal execution of system activities. There are several different options for introducing time and time passing in system descriptions: durationless ...
Alessandro Aldini   +2 more
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Some Purely Deterministic Processes

2011
The linear prediction problem as it arises in the case of stationary processes has attracted much attention. The problem has been studied most intensively when the prediction error is known to be positive. It is of some interest to consider a few simple situations in which the prediction error is zero, especially as a situation of this sort arises in ...
Richard A. Davis   +2 more
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Spectral Analysis of Deterministic Process

2017
This chapter analyzes a deterministic process in the frequency domain via Fourier series (for period process) and Fourier Transform (for non-period process). Estimators based on a sample time history of the process are introduced and their possible distortions arising from finite sampling rate (aliasing) and duration (leakage) are discussed.
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