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Extending the Wong-Zakai theorem to reversible Markov processes

Richard F. Bass, B. Hambly, Terry Lyons (2002)

Journal of the European Mathematical Society

We show how to construct a canonical choice of stochastic area for paths of reversible Markov processes satisfying a weak Hölder condition, and hence demonstrate that the sample paths of such processes are rough paths in the sense of Lyons. We further prove that certain polygonal approximations to these paths and their areas converge in p -variation norm. As a corollary of this result and standard properties of rough paths, we are able to provide a significant generalization of the classical result...

Extensión de medidas difusas usando la esperanza monótona.

Manuel Jorge Bolaños Carmona, María Teresa Lamata Jiménez, Serafín Moral Callejón (1987)

Stochastica

The monotone expectation is defined as a functional over fuzzy measures on finite sets. The functional is based on Choquet functional over capacities and its more relevant properties are proved, including the generalization of classical mathematical expectation and Dempster's upper and lower expectations of an evidence. In second place, the monotone expectation is used to define measures of fuzzy sets. Such measures are compared with the ones based on Sugeno integral. Finally, we prove a generalization...

Extension of stochastic dominance theory to random variables

Chi-Kwong Li, Wing-Keung Wong (2010)

RAIRO - Operations Research

In this paper, we develop some stochastic dominance theorems for the location and scale family and linear combinations of random variables and for risk lovers as well as risk averters that extend results in Hadar and Russell (1971) and Tesfatsion (1976). The results are discussed and applied to decision-making.

Extension to copulas and quasi-copulas as special 1 -Lipschitz aggregation operators

Erich Peter Klement, Anna Kolesárová (2005)

Kybernetika

Smallest and greatest 1 -Lipschitz aggregation operators with given diagonal section, opposite diagonal section, and with graphs passing through a single point of the unit cube, respectively, are determined. These results are used to find smallest and greatest copulas and quasi-copulas with these properties (provided they exist).

Extrapolation in fractional autoregressive models

Jiří Anděl, Georg Neuhaus (1998)

Kybernetika

The naïve and the least-squares extrapolation are investigated in the fractional autoregressive models of the first order. Some explicit formulas are derived for the one and two steps ahead extrapolation.

Extremal and additive processes generated by Pareto distributed random vectors

Kosto V. Mitov, Saralees Nadarajah (2014)

ESAIM: Probability and Statistics

Pareto distributions are most popular for modeling heavy tailed data. Here, we obtain weak limits of a sequence of extremal and a sequence of additive processes constructed by a series of Bernoulli point processes with bivariate Pareto space components. For the limiting processes we derive the one dimensional distributions in explicit forms. Some of the main properties of these distributions are also proved.

Extremal and optimal solutions in the transshipment problem

Viktor Beneš (1992)

Commentationes Mathematicae Universitatis Carolinae

The paper yields an investigation of the set of all finite measures on the product space with given difference of marginals. Extremal points of this set are characterized and constructed. Sets of uniqueness are studied in the relation to marginal problem. In the optimization problem the support of the optimal measure is described for a class of cost functions. In an example the optimal value is reached by an unbounded sequence of measures.

Extremal (in)dependence of a maximum autoregressive process

Marta Ferreira (2013)

Discussiones Mathematicae Probability and Statistics

Maximum autoregressive processes like MARMA (Davis and Resnick, [5] 1989) or power MARMA (Ferreira and Canto e Castro, [12] 2008) have singular joint distributions, an unrealistic feature in most applications. To overcome this pitfall, absolute continuous versions were presented in Alpuim and Athayde [2] (1990) and Ferreira and Canto e Castro [14] (2010b), respectively. We consider an extended version of absolute continuous maximum autoregressive processes that accommodates both asymptotic tail...

Extremal points of high-dimensional random walks and mixing times of a brownian motion on the sphere

Ronen Eldan (2014)

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

We derive asymptotics for the probability that the origin is an extremal point of a random walk in ℝ n . We show that in order for the probability to be roughly 1 / 2 , the number of steps of the random walk should be between e n / ( C log n ) and e C n log n for some constant C g t ; 0 . As a result, we attain a bound for the π 2 -covering time of a spherical Brownian motion.

Extremal problems for conditioned brownian motion and the hyperbolic metric

Rodrigo Bañuelos, Tom Carroll (2000)

Annales de l'institut Fourier

This paper investigates isoperimetric-type inequalities for conditioned Brownian motion and their generalizations in terms of the hyperbolic metric. In particular, a generalization of an inequality of P. Griffin, T. McConnell and G. Verchota, concerning extremals for the lifetime of conditioned Brownian motion in simply connected domains, is proved. The corresponding lower bound inequality is formulated in various equivalent forms and a special case of these is proved.

Extremal solutions of a general marginal problem

Petra Linhartová (1991)

Commentationes Mathematicae Universitatis Carolinae

The characterization of extremal points of the set of probability measures with given marginals is given in the general context of a marginal system. The sets of marginal uniqueness are studied and an example is added to illustrate the theory.

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