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On differential equations and inclusions with mean derivatives on a compact manifold

S.V. Azarina, Yu.E. Gliklikh (2007)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We introduce and investigate a new sort of stochastic differential inclusions on manifolds, given in terms of mean derivatives of a stochastic process, introduced by Nelson for the needs of the so called stochastic mechanics. This class of stochastic inclusions is ideologically the closest one to ordinary differential inclusions. For inclusions with forward mean derivatives on manifolds we prove some results on the existence of solutions.

On distributions of order statistics for absolutely continuous copulas with applications to reliability

Piotr Jaworski, Tomasz Rychlik (2008)

Kybernetika

Performance of coherent reliability systems is strongly connected with distributions of order statistics of failure times of components. A crucial assumption here is that the distributions of possibly mutually dependent lifetimes of components are exchangeable and jointly absolutely continuous. Assuming absolute continuity of marginals, we focus on properties of respective copulas and characterize the marginal distribution functions of order statistics that may correspond to absolute continuous...

On ℝd-valued peacocks

Francis Hirsch, Bernard Roynette (2013)

ESAIM: Probability and Statistics

In this paper, we consider ℝd-valued integrable processes which are increasing in the convex order, i.e. ℝd-valued peacocks in our terminology. After the presentation of some examples, we show that an ℝd-valued process is a peacock if and only if it has the same one-dimensional marginals as an ℝd-valued martingale. This extends former results, obtained notably by Strassen [Ann. Math. Stat. 36 (1965) 423–439], Doob [J. Funct. Anal. 2 (1968) 207–225] and Kellerer [Math. Ann. 198 (1972) 99–122].

On elliptic curves and random matrix theory

Mark Watkins (2008)

Journal de Théorie des Nombres de Bordeaux

Rubinstein has produced a substantial amount of data about the even parity quadratic twists of various elliptic curves, and compared the results to predictions from random matrix theory. We use the method of Heegner points to obtain a comparable (yet smaller) amount of data for the case of odd parity. We again see that at least one of the principal predictions of random matrix theory is well-evidenced by the data.

On entropies for random partitions of the unit segment

Milena Bieniek, Dominik Szynal (2008)

Kybernetika

We prove the complete convergence of Shannon’s, paired, genetic and α-entropy for random partitions of the unit segment. We also derive exact expressions for expectations and variances of the above entropies using special functions.

On entropy and Hausdorff dimension of measures defined through a non-homogeneous Markov process

Athanasios Batakis (2006)

Colloquium Mathematicae

We study the Hausdorff dimension of measures whose weight distribution satisfies a Markov non-homogeneous property. We prove, in particular, that the Hausdorff dimensions of this kind of measures coincide with their lower Rényi dimensions (entropy). Moreover, we show that the packing dimensions equal the upper Rényi dimensions. As an application we get a continuity property of the Hausdorff dimension of the measures, when viewed as a function of the distributed weights under the ℓ ∞ norm.

Currently displaying 261 – 280 of 1206