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Upgrading Probability via Fractions of Events

Roman Frič, Martin Papčo (2016)

Communications in Mathematics

The influence of “Grundbegriffe” by A. N. Kolmogorov (published in 1933) on education in the area of probability and its impact on research in stochastics cannot be overestimated. We would like to point out three aspects of the classical probability theory “calling for“ an upgrade: (i) classical random events are black-and-white (Boolean); (ii) classical random variables do not model quantum phenomena; (iii) basic maps (probability measures and observables – dual maps to random variables) have very...

Upper bound for the non-maximal eigenvalues of irreducible nonnegative matrices

Xiao-Dong Zhang, Rong Luo (2002)

Czechoslovak Mathematical Journal

We present a lower and an upper bound for the second smallest eigenvalue of Laplacian matrices in terms of the averaged minimal cut of weighted graphs. This is used to obtain an upper bound for the real parts of the non-maximal eigenvalues of irreducible nonnegative matrices. The result can be applied to Markov chains.

Upper bounds for the density of solutions to stochastic differential equations driven by fractional brownian motions

Fabrice Baudoin, Cheng Ouyang, Samy Tindel (2014)

Annales de l'I.H.P. Probabilités et statistiques

In this paper we study upper bounds for the density of solution to stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H g t ; 1 / 3 . We show that under some geometric conditions, in the regular case H g t ; 1 / 2 , the density of the solution satisfies the log-Sobolev inequality, the Gaussian concentration inequality and admits an upper Gaussian bound. In the rough case H g t ; 1 / 3 and under the same geometric conditions, we show that the density of the solution is smooth and admits an upper...

Upper large deviations for maximal flows through a tilted cylinder

Marie Theret (2014)

ESAIM: Probability and Statistics

We consider the standard first passage percolation model in ℤd for d ≥ 2 and we study the maximal flow from the upper half part to the lower half part (respectively from the top to the bottom) of a cylinder whose basis is a hyperrectangle of sidelength proportional to n and whose height is h(n) for a certain height function h. We denote this maximal flow by τn (respectively φn). We emphasize the fact that the cylinder may be tilted. We look at the probability that these flows, rescaled by the surface...

Upper tails of self-intersection local times of random walks: survey of proof techniques

Wolfgang König (2010)

Actes des rencontres du CIRM

The asymptotics of the probability that the self-intersection local time of a random walk on ℤ d exceeds its expectation by a large amount is a fascinating subject because of its relation to some models from Statistical Mechanics, to large-deviation theory and variational analysis and because of the variety of the effects that can be observed. However, the proof of the upper bound is notoriously difficult and requires various sophisticated techniques. We survey some heuristics and some recently elaborated...

Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes

Daskalova, Nina (2010)

Serdica Journal of Computing

Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are particles of different types. Usually such a process is not observable in the sense of the whole tree, but only as the “generation” at a given moment in time, which consists of the number of particles of every type. This requires an EM-type algorithm to obtain a maximum likelihood (ML) estimate of the parameters of the branching process. Using a version of the inside-outside algorithm for stochastic context-free...

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