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The Measurable Space of Stochastic Processes

2010 Seventh International Conference on the Quantitative Evaluation of Systems, 2010
We introduce a stochastic extension of CCS endowed with structural operational semantics expressed in terms of measure theory. The set of processes is organised as a measurable space by the sigma-algebra generated by structural congruence. The structural operational semantics associates to each process a set of measures over the space of processes. The
Cardelli, Luca, Mardare, Radu
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Stochastic Measure Processes

1981
Stochastic measure processes arise as mathematical models of the evolution of spatially distributed populations under conditions in which fluctuations are of importance. Models of this type have arisen in several fields including nonequilibrium statistical physics [30], chemical kinetics [30], population genetics [16], ecology [31], epidemiology and ...
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Measurement in stochastic mechanics

Journal of Mathematical Physics, 1981
Stochastic mechanics is an explanation of nonrelativistic quantum phenomena in terms of stochastic differential equations. In this note a simple example of a measurement is constructed and the behavior of the sample paths of the corresponding stochastic differential equation is examined.
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Product Stochastic Measures.

1985
Abstract : The concept of symmetric tensor product of a Hilbert space is used to construct a product measure of orthogonally scattered measures. The result is applied to the construction of an sq L-valued product stochastic measure (p.s.m.) of non-identically distributed sq-L-valued independently scattered measures.
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Information measures quantifying aperiodic stochastic resonance

Physical Review E, 1996
Aperiodic stochastic resonance ~ASR! is a phenomenon in which the response of a nonlinear system to a subthreshold information-bearing signal is optimized by the presence of noise. We have previously characterized this effect by the use of cross-correlation-based measures. Here we apply a measure ~transinformation!
, Heneghan   +5 more
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On Measurable Modification of Stochastic Functions

Theory of Probability & Its Applications, 2002
A few criteria for the existence of a measurable modification are considered. If the function \(\zeta_t\), \(t\in T\), is stochastically continuous, i.e. for all \(\varepsilon > 0\), \[ P\{|\xi_t-\xi_{t_0}|\geq \varepsilon\}=\iint_{|x-y|\geq\varepsilon} P_{t,t_0}(dxdy)\to 0,\qquad t-t_0\in T,\tag{1} \] then a measurable modification exists [cf. \textit{
Di Nunno, G., Rozanov, Yu. A.
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Stochastic Dissipative PDE's and Gibbs Measures

Communications in Mathematical Physics, 2000
This paper concerns a class of dissipative nonlinear PDE's forced by a random perturbation with the state space varying in a bounded domain. The analysis covers the following items: 1. Preliminary: 1.1. Invariant measures for a class of Markov chains, 1.2. Stationary process corresponding to an invariant measure, 1.3 Gibbs system; 2. Invariant measures
Kuksin, Sergei, Shirikyan, Armen
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On a Measure of Stochastic Dependence

Theory of Probability & Its Applications, 1962
An explicit expression is found for the amount of information (in the sense of A. N. Kolmogorov) about one $\sigma $-subalgebra contained in another $\sigma $-subalgebra of an abstract algebra with a probability measure. The formula obtained is generalized to a system of subalgebras of any cardinal number.
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Stochastic Measures and Integrals

1987
The usual tools of mathematical analysis and of the theory of ordinary differential equations cannot be applied to random functions of the type of the Brownian motion process, which arise in several branches of probability theory and are important for application. The reason is that these functions turn out to be not differentiable.
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Time to add screening for financial hardship as a quality measure?

Ca-A Cancer Journal for Clinicians, 2021
Cathy J Bradley   +2 more
exaly  

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