In this note we discuss upper and lower bound for the ruin probability in an insurance model with... more In this note we discuss upper and lower bound for the ruin probability in an insurance model with very heavy-tailed claims and interarrival times.
International Journal of Pure and Applied Mathematics
The article proposes a new standpoint to the cluster validation problem based on a fractal dimens... more The article proposes a new standpoint to the cluster validation problem based on a fractal dimension cluster quality model. The suggested method uses the fractal property to describe cluster geometrical configuration. This notion is applied for further exploration of cluster validity, assuming that its low variability, calculated via different samples, can indicate stable partitions. In the framework of this model, the goodness of a partition is characterized by the quality of mixing two random samples within the partition's clusters. It is implicitly assumed that the quality of a cluster is reflected by its fractal dimensionality estimated via different samples. Valid results are obtained by repeating these calculations on sufficiently large amount of samples drawn. Hence, empirical distributions of the absolute values of the fractal dimension differences are constructed. The distribution most concentrated at the origin is proposed to indicate the true number of clusters. Numerical experiments are presented for various datasets.
In this paper we describe the class of holomorphic generators of semigroups on the unit disk havi... more In this paper we describe the class of holomorphic generators of semigroups on the unit disk having boundary fixed point. In particular, we study the asymptotic behavior of semigroups of hyperbolic type. A classical problem of branching processes is to find conditions providing the convergence of exponential type. We give a geometrical solution of this problem in terms of the Robertson class of starlike functions with respect to a boundary point.
We discuss a new approach for the proof of the Levy-Khintchine formula for the V -infinitely divi... more We discuss a new approach for the proof of the Levy-Khintchine formula for the V -infinitely divisible laws. Our proof is based on a description of the conditionally positive definite functions as positive functionals on semi-normed algebras of suitable test functions. In the framework of this approach we obtain integral representations of the common continuous positive definite functions and the logarithms of characteristic functions of the ordinary infinitely divisible and V -infinitely divisible distribution.
In this note we discuss upper and lower bound for the ruin probability in an insurance model with... more In this note we discuss upper and lower bound for the ruin probability in an insurance model with very heavy-tailed claims and interarrival times.
International Journal of Pure and Applied Mathematics
The article proposes a new standpoint to the cluster validation problem based on a fractal dimens... more The article proposes a new standpoint to the cluster validation problem based on a fractal dimension cluster quality model. The suggested method uses the fractal property to describe cluster geometrical configuration. This notion is applied for further exploration of cluster validity, assuming that its low variability, calculated via different samples, can indicate stable partitions. In the framework of this model, the goodness of a partition is characterized by the quality of mixing two random samples within the partition's clusters. It is implicitly assumed that the quality of a cluster is reflected by its fractal dimensionality estimated via different samples. Valid results are obtained by repeating these calculations on sufficiently large amount of samples drawn. Hence, empirical distributions of the absolute values of the fractal dimension differences are constructed. The distribution most concentrated at the origin is proposed to indicate the true number of clusters. Numerical experiments are presented for various datasets.
In this paper we describe the class of holomorphic generators of semigroups on the unit disk havi... more In this paper we describe the class of holomorphic generators of semigroups on the unit disk having boundary fixed point. In particular, we study the asymptotic behavior of semigroups of hyperbolic type. A classical problem of branching processes is to find conditions providing the convergence of exponential type. We give a geometrical solution of this problem in terms of the Robertson class of starlike functions with respect to a boundary point.
We discuss a new approach for the proof of the Levy-Khintchine formula for the V -infinitely divi... more We discuss a new approach for the proof of the Levy-Khintchine formula for the V -infinitely divisible laws. Our proof is based on a description of the conditionally positive definite functions as positive functionals on semi-normed algebras of suitable test functions. In the framework of this approach we obtain integral representations of the common continuous positive definite functions and the logarithms of characteristic functions of the ordinary infinitely divisible and V -infinitely divisible distribution.
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Papers by Zeev Volkovich