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In the present paper, we give a probabilistic characterization of U1(D) and a probabilistic representation of u∈U1(D) in terms of a superdiffusion.
We also give a probabilistic interpretation of this solution in terms of backward doubly stochastic differential equations formulated in a weak sense.
The consumption and generation models are then combined to give a probabilistic estimate of their combined effect in the long term using Monte Carlo simulations.
In present paper the authors are focusing on the features of the orientation distribution function (ODF), used to give a probabilistic assessment to the orientation of fibres in fibre reinforced composites.
Here we give a probabilistic proof of relative Fatou's theorem for α/2-harmonic functions (equivalently for symmetric α-stable processes) in bounded κ-fat open set where α∈ 0,2).
This paper presents a methodology for carrying out statistical analysis of electricity consumption and distributed wind generation in distribution systems in order to investigate their combined effect, e.g., to give a probabilistic estimate of the effective peak net load.
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Recently, Chang and Xu gave a probabilistic proof of a combinatorial identity which involves binomial coefficients.
In particular this gives a probabilistic representation of some symmetric Markov semigroups considered by Davies and Lindsay.
Given a probabilistic world model, an important problem is to find the maximum a-posteriori probability (MAP) instantiation of all the random variables given the evidence.
Consideration-2 Given a probabilistic polynomial time adversary A, he asks the challenger B for the cipher-text of his queried keywords for t times.
Consideration-1 Given a probabilistic polynomial time adversary A, he asks the challenger B for the cipher-text of his submitted keywords for polynomial times.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com