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The present paper is a continuation of the work, carried out in [4] and [5] of investigating the relationship between a Gaussian process and its reproducing kernel Hilbert subspace. Our main result gives a characterization of the topological support of a Gaussian measure defined on a linear topological space of functions on an arbitrary set. As special cases we consider Gaussian processes on Ba...

In this paper, the largest and the smallest observations are considered, at the time when a new record of either kind (upper or lower) occurs based on a sequence of independent random variables with identical continuous distributions. We prove that sequences of the residual or past entropy of the current records characterizes F in the family of continuous distributions. The exponential and the ...

In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ wi...

This paper investigates calculus rules for the limiting Fréchet-subdifferential of infimum value functions of locally Lipschitzian and non-Lipschitzian functions. It is not required that the infimum is attained.

Received (received date) Revised (revised date) Communicated by (Name) The article analyzes similarity of closed polygonal curves with respect to the Fréchet metric, which is stronger than the well-known Hausdorff metric and therefore is more appropriate in some applications. An algorithm is described that determines whether the Fréchet distance between two closed polygonal curves with m and n ...

Connections between Bayesian nonparametric inference and the classes of prob-ability measures with known marginals (Frechet classes) are investigated. Inparticular, a class of Dirichlet processes with parameters proportional to prob-ability measures in a Frechet class will be considered.Relations between two statistical characters are then studied, by presentinga...