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On the local time density of the reflecting Brownian bridge
 MR MR1768499 (2001h:60134
, 2000
"... Expressions for the multidimensional densities of Brownian bridge local time are derived by two different methods: A direct method based on Kac’s formula for Brownian functionals and an indirect one based on a limit theorem for strata of random mappings. ..."
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Expressions for the multidimensional densities of Brownian bridge local time are derived by two different methods: A direct method based on Kac’s formula for Brownian functionals and an indirect one based on a limit theorem for strata of random mappings.
On The Number Of Predecessors In Constrained Random Mappings
 Stat. Probab. Letters
, 1997
"... We consider random mappings from an nelement set into itself with constraints on coalescence as introduced by Arney and Bender. A local limit theorem for the distribution of the number of predecessors of a random point in such a mapping is presented by using a generating function approach and sing ..."
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We consider random mappings from an nelement set into itself with constraints on coalescence as introduced by Arney and Bender. A local limit theorem for the distribution of the number of predecessors of a random point in such a mapping is presented by using a generating function approach and singularity analysis. 1.
A Poisson * geometric convolution law for the number of components in unlabelled combinatorial structures
 COMBIN., PROBAB. AND COMPUT
, 1995
"... Given a class of combinatorial structures C, we consider the quantity N(n; m), the number of multiset constructions P (of C) of size n having exactly m Ccomponents. Under general ..."
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Given a class of combinatorial structures C, we consider the quantity N(n; m), the number of multiset constructions P (of C) of size n having exactly m Ccomponents. Under general
The Number Of Descendants In Simply Generated Random Trees
, 1999
"... We derive asymptotic results on the distribution of the number of descendants in simply generated trees. Our method is based on a generating function approach and complex contour integration. 1. ..."
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We derive asymptotic results on the distribution of the number of descendants in simply generated trees. Our method is based on a generating function approach and complex contour integration. 1.
ON MOMENT SEQUENCES AND MIXED POISSON DISTRIBUTIONS
, 1403
"... ABSTRACT. In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a nonnegative random variable X with moment sequence (µs)s∈N we determine a discrete random variable Y, whose moment sequence is given by the Stirling transform o ..."
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ABSTRACT. In this article we survey properties of mixed Poisson distributions and probabilistic aspects of the Stirling transform: given a nonnegative random variable X with moment sequence (µs)s∈N we determine a discrete random variable Y, whose moment sequence is given by the Stirling transform of the sequence (µs)s∈N, and identify the distribution as a mixed Poisson distribution. We discuss properties of this family of distributions and present a simple limit theorem based on expansions of factorial moments. Moreover, we present several examples of mixed Poisson distributions in the analysis of random discrete structures, unifying and extending earlier results. We also add several entirely new results: we analyze triangular urn models, where the initial configuration or the dimension of the urn is not fixed, but may depend on the discrete time n. We discuss the branching structure of planeoriented recursive trees and its relation to table sizes in the Chinese restaurant process. Furthermore, we discuss root isolation procedures in Cayley trees, a parameter in parking functions, zero contacts in lattice paths consisting of bridges, and a parameter related to cyclic points and trees in graphs of random mappings, all leading to mixed PoissonRayleigh distributions. Finally, we indicate how mixed Poisson distributions naturally arise in the critical composition scheme of Analytic Combinatorics. 1.
The Parity of the SumofDigitsFunction of Generalized Zeckendorf Representations
"... this paper is to discuss the partial sums ..."
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Probabilistic Analysis of a Schröder Walk Generation Algorithm
, 2000
"... Using some tools from Combinatorics, Probability Theory, and Singularity analysis, we present a complete asymptotic probabilistic analysis of the cost of a Schröder walk generation algorithm proposed by Penaud et al.([13] ). Such a walk S(:) is made of northeast, southeast and east steps, but each e ..."
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Using some tools from Combinatorics, Probability Theory, and Singularity analysis, we present a complete asymptotic probabilistic analysis of the cost of a Schröder walk generation algorithm proposed by Penaud et al.([13] ). Such a walk S(:) is made of northeast, southeast and east steps, but each east step is made of two time units (if we consider recording the time t on the abscissa and the moves on the ordinates). The walk starts from the origin at time 0, cannot go under the time axis, and we add the constraint S(2n) = 0. Five different probability distributions will appear in the study: Gaussian, Exponential, Geometric, Rayleigh and a new probability distribution, that we can characterize by its density Laplace Transform and its moments.
Journal of Applied Mathematics and Stochastic Analysis, 13:2 (2000), 125136. ON THE LOCAL TIME DENSITY OF THE REFLECTING BROWNIAN BRIDGE
, 1999
"... Expressions for the multidimensional densities of Brownian bridge local time are derived by two different methods: A direct method based on Kac’s formula for Brownian functionals and an indirect one based on a limit theorem for strata of random mappings. ..."
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Expressions for the multidimensional densities of Brownian bridge local time are derived by two different methods: A direct method based on Kac’s formula for Brownian functionals and an indirect one based on a limit theorem for strata of random mappings.