Sobre la regularidad de ecuaciones integrales estocásticas hilbertianas de tipo cabaña.
Estudio del carácter markoviano fuerte y regularidades de la solución de ecuaciones integrales estocásticas Ito generalizadas.
El objetivo de este trabajo es un estudio sobre los caracteres felleriano y markoviano fuerte y las propiedades de regularidad del proceso solución de una ecuación integral estocástica generalizada (tipo Ito), pero generalizada en el sentido de considerar una formulación en términos de procesos operador-valuados. Esta formulación generaliza simultánea e independientemente las integrales de Cabaña y Daletsky.
Propiedades de regularidad de ecuaciones integrales estocásticas de tipo Cabaña, sobre espacios de Hilbert separables.
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.
Jacobians of certain transformations of singular matrices
In this study various Jacobians of transformations of singular random matrices are found. An alternative proof of Uhlig's first conjecture (Uhlig (1994)) is proposed. Furthermore, we propose various extensions of this conjecture under different singularities. Finally, an application of the theory of singular distributions is discussed.
On the Karhunen-Loeve expansion for transformed processes.
We discuss the influence of the transformation {X(t)} → {f(t) X(τ(t))} on the Karhunen-Loève expansion of {X(t)}. Our main result is that, in general, the Karhunen-Loève expansion of {X(t)} with respect to Lebesgue's measure is transformed in the Karhunen-Loève expansion of {f(t) X(τ(t))} with respect to the measure f(t)dτ(t). Applications of this result are given in the case of Wiener process, Brownian bridge, and Ornstein-Uhlenbeck process.
Characterizacion of the bivariate discrete distributions defined by a partial difference equations system.
Conditions under which the solutions of a partial difference equations system can be probability functions are examined. When the coefficients of the system are polynomials then the partial difference equations system satisfied by generating functions associated to these distributions are easily obtained; they give useful recurrence relations for the moments. Three examples are given as well.
On the estimation of the drift coefficient in diffusion processes with random stopping times.
This paper considers stochastic differential equations with solutions which are multidimensional diffusion processes with drift coefficient depending on a parametric vector θ. By considering a trajectory observed up to a stopping time, the maximum likelihood estimator for θ has been obtained and its consistency and asymptotic normality have been proved.
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