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Properties of generalized set-valued stochastic integrals

Michał Kisielewicz (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The paper is devoted to properties of generalized set-valued stochastic integrals defined in [10]. These integrals generalize set-valued stochastic integrals defined by E.J. Jung and J.H. Kim in the paper [4]. Up to now we were not able to construct any example of set-valued stochastic processes, different on a singleton, having integrably bounded set-valued integrals defined in [4]. It was shown by M. Michta (see [11]) that in the general case set-valued stochastic integrals defined by E.J. Jung...

Properties of local-nondeterminism of Gaussian and stable random fields and their applications

Yimin Xiao (2006)

Annales de la faculté des sciences de Toulouse Mathématiques

In this survey, we first review various forms of local nondeterminism and sectorial local nondeterminism of Gaussian and stable random fields. Then we give sufficient conditions for Gaussian random fields with stationary increments to be strongly locally nondeterministic (SLND). Finally, we show some applications of SLND in studying sample path properties of ( N , d ) -Gaussian random fields. The class of random fields to which the results are applicable includes fractional Brownian motion, the Brownian...

Properties of set-valued stochastic integrals

Jerzy Motyl, Joachim Syga (2006)

Discussiones Mathematicae Probability and Statistics

We introduce set-valued stochastic integrals driven by a square-integrable martingale and by a semimartingale. We investigate properties of both integrals.

Properties of the induced semigroup of an Archimedean copula

Włodzimierz Wysocki (2004)

Applicationes Mathematicae

It is shown that to every Archimedean copula H there corresponds a one-parameter semigroup of transformations of the interval [0,1]. If the elements of the semigroup are diffeomorphisms, then it determines a special function v H called the vector generator. Its knowledge permits finding a pseudoinverse y = h(x) of the additive generator of the Archimedean copula H by solving the differential equation d y / d x = v H ( y ) / x with initial condition ( d h / d x ) ( 0 ) = - 1 . Weak convergence of Archimedean copulas is characterized in terms of vector...

Propiedades de regularidad de ecuaciones integrales estocásticas de tipo Cabaña, sobre espacios de Hilbert separables.

Ramón Gutiérrez Jáimez, Josefa Linares Pérez (1985)

Trabajos de Estadística e Investigación Operativa

En este trabajo consideramos ecuaciones integrales estocásticas tipo Ito, que son construidas con integral estocástica de Cabaña, sobre espacios de Hilbert separables y respecto de operadores de Wiener. Se estudian las propiedades de regularidad del proceso solución, analizando su comportamiento respecto de la variación de los coeficientes de la ecuación y de las condiciones iniciales.

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