1,720,981 research outputs found
On the sum of independent generalized Mittag–Leffler random variables and the related fractional processes
No full textWe obtain the distribution of the sum of independent and non-identically distributed generalized Mittag–Leffler random variables. We then apply this result to study some related fractional point processes. We present their explicit probability mass functions as well as their connections with the fractional integral/differential equations. In the case of a point process with Mittag–Leffler distributed waiting times which alternate two indexes (Formula presented.) and two rates (Formula presented.) we also study the conditional arrival times and we show an application to the telegraph process
A note on the conditional probabilities of the telegraph process
No full textWe consider the telegraph process with two velocities, a1>a2∈R, and two rates of reversal, λ1,λ2>0. We study some of its features with respect to the conditional probability measure where both the initial speed and the number of changes of direction are known. We exhibit a new proof by induction of the (conditional) probability law and a detailed study of the distribution of the motion at time t>0 conditioned on its position at a previous time 00, its maximum and its minimum up to that moment
On the distribution of the maximum of the telegraph process
No full textIn this paper we present the distribution of the maximum of the telegraph process in the cases where the initial velocity is positive or negative with an even and an odd number of velocity reversals. For the telegraph process with positive initial velocity a reflection principle is proved to be valid while in the case of an initial leftward displacement the conditional distributions are perturbed by a positive probability of never visiting the half positive axis. Various relationships are established among the mentioned four classes of conditional distributions of the maximum. The unconditional distributions of the maximum of the telegraph process are obtained for positive and negative initial steps as well as their limiting behaviour. Furthermore the cumulative distributions and the general moments of the conditional maximum are presented
On the exact distributions of the maximum of the asymmetric telegraph process
No full textIn this paper we present the distribution of the maximum of the asymmetric telegraph process in an arbitrary time interval [0,t] under the conditions that the initial velocity V(0) is either c1 or −c2 and the number of changes of direction is odd or even. For the case V(0)=−c2 the singular component of the distribution of the maximum displays an unexpected cyclic behavior and depends only on c1 and c2, but not on the current time t. We obtain also the unconditional distribution of the maximum for either V(0)=c1 or V(0)=−c2 and its expression has the form of series of Bessel functions. We also show that all the conditional distributions emerging in this analysis are governed by generalized Euler–Poisson–Darboux equations. We recover all the distributions of the maximum of the symmetric telegraph process as particular cases of the present paper. We underline that it rarely happens to obtain explicitly the distribution of the maximum of a process. For this reason the results on the range of oscillations of a natural process like the telegraph model make it useful for many applications
Stochastic Dynamics of Generalized Planar Random Motions with Orthogonal Directions
No full textWe study planar random motions with finite velocities, of norm c > 0, along orthogonal directions and changing at the instants of occurrence of a nonhomogeneous Poisson process with rate function lambda = lambda(t), t >= 0. We focus on the distribution of the current position (X(t), Y(t)), t >= 0, in the case where the motion has orthogonal deviations and where also reflection is admitted. In all the cases, the process is located within the closed square S-ct = {(x, y) is an element of R-2 : |x| + |y| <= ct} and we obtain the probability law inside S-ct, on the edge & part;S-ct and on the other possible singularities, by studying the partial differential equations governing all the distributions examined. A fundamental result is that the vector process (X, Y) is probabilistically equivalent to a linear transformation of two (independent or dependent) one-dimensional symmetric telegraph processes with rate function proportional to lambda and velocity c/2. Finally, we extend the results to a wider class of orthogonal-type evolutions
Multidimensional random motions with a natural number of finite velocities
No full textWe present a detailed analysis of random motions moving in higher spaces with a natural number of velocities. In the case of the so-called minimal random dynamics, under some broad assumptions, we give the joint distribution of the position of the motion (for both the inner part and the boundary of the support) and the number of displacements performed with each velocity. Explicit results for cyclic and complete motions are derived. We establish useful relationships between motions moving in different spaces, and we derive the form of the distribution of the movements in arbitrary dimension. Finally, we investigate further properties for stochastic motions governed by non-homogeneous Poisson processes
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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