المنشورات و المؤلفات
Following the model introduced by Aguech et al. (Probab Eng Inf Sci 21:133–141, 2007), the weighted depth of a node in a labelled rooted tree is the sum of all labels on the path connecting the node to the root. We analyse weighted depths of nodes...
We investigate distances between pairs of nodes in digital trees (digital search trees (DST), and tries). By analytic techniques, such as the Mellin Transform and poissonization, we describe a program to determine the moments of these distances. The...
We consider weighted path lengths to the extremal leaves in a random binary search tree. When linearly scaled, the weighted path length to the minimal label has Dickman's infinitely divisible distribution as a limit. By contrast, the weighted path...
Two processes of random fragmentation of an interval are investigated. For each of them, there is a splitting probability at each step of the fragmentation process whose overall effect is to stabilize the global number of splitting events. More...
In this paper we consider a non balanced generalized Polya urn model. At each step, m balls are drawn at random from an urn containing white and black balls. Balls are added according the inspected colors. We consider two different models: the self...
All my results on Probability Theory and application from 1998 to 2009
In this paper, a perturbation expansion technique is introduced to decompose the tracking error of a general adaptive tracking algorithm in a linear regression model. This method allow to obtain tracking error bound but also tight approximate...
In this paper we study a generalized Pólya urn with balls of two colors and a random triangular replacement matrix. We extend some results of Janson (2004), (2005) to the case where the largest eigenvalue of the mean of the replacement matrix is not...
Distances between nodes in random trees is a popular topic, and several classes of trees have recently been investigated. We look into this matter in digital search trees. By analytic techniques, such as the Mellin Transform and poissonization, we...
Let, for each n ∈ N, (Xi,n) 05i5n be a triangular array of stationary, centered, square integrable and associated real valued random variables satisfying the weakly dependence condition lim N→N0 lim sup n→+∞ n Xn r=N Cov (X0,n, Xr,n) = 0; where N0...
In this paper, a perturbation expansion technique is introduced to decompose the tracking error of a general adaptive tracking algorithm in a linear regression model. This method results in a tracking error bound and tight approximate expressions...