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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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MEASURE EVOLUTION FOR "STOCHASTIC FLOWS"

Stochastics and Dynamics, 2008
In this paper we study how σ-finite measures on ℝdevolve under a class of "stochastic flows" associated to stochastic differential equations with (resp. without) jumps in ℝd. First we show the related measure evolution processes are càdlàg (resp. continuous), strongly Markovian and weakly Fellerian.
Wang, Bin, Xiang, Kai-Nan
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Repeated measurements in stochastic mechanics

Physical Review D, 1986
Stochastic mechanics provides a probabilistic scheme for the description of quantum systems. Grabert, Haaumlnggi, and Talkner, and Nelson have pointed out that its multitime correlations seem to be in disagreement with quantum-mechanical predictions.
Blanchard Ph, Golin S, SERVA, Maurizio
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Stochastic Integrals and Differential Measures

Theory of Probability & Its Applications, 1988
The description of the class of measures with square integrable logarithmic derivative along a vector field and an operator field is obtained. This derivative coincides with an extended stochastic integral in the Gaussian case. The proofs are based on integration by parts.
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A stochastic dominance approach to the measurement of discrimination

Journal of Economic Theory, 2012
This paper suggests a bridge between stochastic dominance and discrimination measurement. Discrimination orderings are defined and illustrated through discrimination curves, in the same spirit as stochastic dominance. The main result generalizes the equivalence between Generalized Lorenz dominance and second order stochastic dominance.
Michel Le Breton   +2 more
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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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Efficiency measurement in the stochastic frontier model

European Journal of Operational Research, 2001
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jan Ondrich, John Ruggiero
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Stochastic productivity measurement

Journal of Productivity Analysis, 2008
Stochastic productivity indicators are defined, and superlative measures of these indicators are derived. It is shown that, in the presence of complete markets or a common-expectations equilibrium, differences in the market values of firms are superlative indicators of cross-sectional productivity differences.
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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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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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