Displaying similar documents to “Conditional differential equations”

On d-finite tuples in random variable structures

Shichang Song (2013)

Fundamenta Mathematicae

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We prove that the d-finite tuples in models of ARV are precisely the discrete random variables. Then, we apply d-finite tuples to the work by Keisler, Hoover, Fajardo, and Sun concerning saturated probability spaces. In particular, we strengthen a result in Keisler and Sun's recent paper.

The square model for random groups

Tomasz Odrzygóźdź (2016)

Colloquium Mathematicae

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We introduce a new random group model called the square model: we quotient a free group on n generators by a random set of relations, each of which is a reduced word of length 4. We prove that, just as in the Gromov model, for densities > 1/2 a random group in the square model is trivial with overwhelming probability and for densities < 1/2 a random group is hyperbolic with overwhelming probability. Moreover, we show that for densities d < 1/3 a random group in the square model...

On the product of triangular random variables

Mridula Garg, Sangeeta Choudhary, Saralees Nadarajah (2009)

Applicationes Mathematicae

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We derive the probability density function (pdf) for the product of three independent triangular random variables. It involves consideration of various cases and subcases. We obtain the pdf for one subcase and present the remaining cases in tabular form. We also indicate how to calculate the pdf for the product of n triangular random variables.

Strong disorder in semidirected random polymers

N. Zygouras (2013)

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

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We consider a random walk in a random potential, which models a situation of a random polymer and we study the annealed and quenched costs to perform long crossings from a point to a hyperplane. These costs are measured by the so called Lyapounov norms. We identify situations where the point-to-hyperplane annealed and quenched Lyapounov norms are different. We also prove that in these cases the polymer path exhibits localization.

Cluster continuous time random walks

Agnieszka Jurlewicz, Mark M. Meerschaert, Hans-Peter Scheffler (2011)

Studia Mathematica

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In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW model is useful in physics, to model diffusing particles. Its scaling limit is a time-changed process, whose densities solve an anomalous diffusion equation. This paper develops limit theory and governing equations for cluster CTRW, in which a random number of jumps cluster together into a single jump. The clustering introduces a dependence between the waiting times and jumps that significantly...

A note on correlation coefficient between random events

Czesław Stępniak (2015)

Discussiones Mathematicae Probability and Statistics

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Correlation coefficient is a well known measure of (linear) dependence between random variables. In his textbook published in 1980 L.T. Kubik introduced an analogue of such measure for random events A and B and studied its basic properties. We reveal that this measure reduces to the usual correlation coefficient between the indicator functions of A and B. In consequence the resuts by Kubik are obtained and strenghted directly. This is essential because the textbook is recommended by...

On gradient-like random dynamical systems

Aya Hmissi, Farida Hmissi, Mohamed Hmissi (2012)

ESAIM: Proceedings

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This paper deals with some characterizations of gradient-like continuous random dynamical systems (RDS). More precisely, we establish an equivalence with the existence of random continuous section or with the existence of continuous and strict Liapunov function. However and contrary to the deterministic case, parallelizable RDS appear as a particular case of gradient-like RDS. The obtained results are generalizations of well-known analogous theorems in the framework of deterministic...