1,721,022 research outputs found
Two-sided exit problem for a spectrally negative -stable Ornstein-Uhlenbeck process and the Wright's generalized hypergeometric functions
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Jacobi Processes with Jumps as Neuronal Models: A First Passage Time Analysis
Full text linkTo overcome some limits of classical neuronal models, we propose a Markovian generalization of the classical model based on Jacobi processes by introducing downwards jumps to
describe the activity of a single neuron. The statistical analysis of inter-spike intervals is performed
by studying the first-passage times of the proposed Markovian Jacobi process with jumps through a
constant boundary. In particular, we characterize its Laplace transform which is expressed in terms
of some generalization of hypergeometric functions that we introduce, and deduce a closed-form
expression for its expectation. Our approach, which is original in the context of first passage time
problems, relies on intertwining relations between the semigroups of the classical Jacobi process
and its generalization, which have been recently established in [11]. A numerical investigation of
the firing rate of the considered neuron is performed for some choices of the involved parameters
and of the jumps distributions
Infinite divisibility of solutions to some self-similar integro-differential equations and exponential functionals of Lévy processes
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q-invariant functions for some generalizations of the Ornstein-Uhlenbeck semigroup
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Exponential functional of a new family of Lévy processes and self-similar continuous state branching processes with immigration
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Law of the exponential functional of one-sided Lévy processes and Asian
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On the joint law of the L-1 and L-2 norms of a 3-dimensional Bessel bridge
No full textWe give an analytical expression for the joint Laplace transform of the L-1 and L-2 norms of a 3-dimensional Bessel bridge. We derive the results by using merely probabilistic arguments. More precisely we show that the law of this functional is closely connected with the one of the first passage time of an Ornstein-Uhlenbeck process. The motivation for studying this problem are multiple; as an instance, they include the computation of the density of the first passage time of Brownian motion over some moving boundaries such as the square root and the quadratic ones
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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