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NonUniform Random Variate Generation
, 1986
"... Abstract. This is a survey of the main methods in nonuniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various ..."
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Cited by 620 (21 self)
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Abstract. This is a survey of the main methods in nonuniform random variate generation, and highlights recent research on the subject. Classical paradigms such as inversion, rejection, guide tables, and transformations are reviewed. We provide information on the expected time complexity of various algorithms, before addressing modern topics such as indirectly specified distributions, random processes, and Markov chain methods.
A survey of maxtype recursive distributional equations
 Annals of Applied Probability 15 (2005
, 2005
"... In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X d = g((ξi,Xi), i ≥ 1). Here(ξi) and g(·) are given and the Xi are independent cop ..."
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Cited by 63 (6 self)
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In certain problems in a variety of applied probability settings (from probabilistic analysis of algorithms to statistical physics), the central requirement is to solve a recursive distributional equation of the form X d = g((ξi,Xi), i ≥ 1). Here(ξi) and g(·) are given and the Xi are independent copies of the unknown distribution X. We survey this area, emphasizing examples where the function g(·) is essentially a “maximum ” or “minimum” function. We draw attention to the theoretical question of endogeny: inthe associated recursive tree process X i,aretheX i measurable functions of the innovations process (ξ i)? 1. Introduction. Write
A note on the approximation of perpetuities
 In Proceedings of 2007 Conference on Analysis of Algorithms, (AofA’07) Juanlespins
, 2007
"... We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the perpetuity. We significantly reduce the complexity of the earlier al ..."
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Cited by 6 (4 self)
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We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the perpetuity. We significantly reduce the complexity of the earlier algorithm. Also one particular perpetuity arising in the analysis of the selection algorithm Quickselect is studied in more detail. Our approach works well for distribution functions. For densities we have weaker error bounds although computer experiments indicate that densities can also be well approximated.
Bivariate uniqueness and endogeny for recursive distributional equations: Two examples
, 2004
"... In this work we prove the bivariate uniqueness property for two “maxtype” recursive distributional equations which then lead to the proof of endogeny for the associated recursive tree processes. Thus providing two concrete instances of the general theory developed by Aldous and Bandyopadhyay [3]. Th ..."
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Cited by 1 (1 self)
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In this work we prove the bivariate uniqueness property for two “maxtype” recursive distributional equations which then lead to the proof of endogeny for the associated recursive tree processes. Thus providing two concrete instances of the general theory developed by Aldous and Bandyopadhyay [3]. The first example discussed here deals with the construction of a frozen percolation process on a infinite regular binary tree. For this we prove that the construction do not involve any external randomness. It is also shown that same is true for any rregular tree and more interestingly for any infinite regular GaltonWatson branching process trees with mild moment condition on the progeny distribution. The second example is proving the endogeny for the Logistic recursive distributional equation which appears for studying the asymptotic limit of the random assignment problem using localweak convergence method. The two examples are quite unrelated and hence illustrate a broad range of applicability of the general methods of [3].
The Double CFTP method
, 2010
"... Abstract. We consider the problem of the exact simulation of random variables Z that satisfy the distributional identity Z L = V Y + (1 − V)Z, where V ∈ [0, 1] and Y are independent, and L = denotes equality in distribution. Equivalently, Z is the limit of a Markov chain driven by that map. We give ..."
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Cited by 1 (0 self)
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Abstract. We consider the problem of the exact simulation of random variables Z that satisfy the distributional identity Z L = V Y + (1 − V)Z, where V ∈ [0, 1] and Y are independent, and L = denotes equality in distribution. Equivalently, Z is the limit of a Markov chain driven by that map. We give an algorithm that can be automated under the condition that we have a source capable of generating independent copies of Y, and that V has a density that can be evaluated in a black box format. The method uses a doubling trick for inducing coalescence in coupling from the past. Applications include exact samplers for many Dirichlet means, some twoparameter Poisson–Dirichlet means, and a host of other distributions related to occupation times of Bessel bridges that can be described by stochastic fixed point equations. Keywords and phrases. Random variate generation. Perpetuities. Coupling from the past. Random partitions. Stochastic recurrences. Stochastic fixed point equations. Distribution theory. Markov chain Monte Carlo. Simulation. Expected time analysis. Bessel bridge. PoissonDirichlet. Dirichlet means.
Analysis of Algorithms (AofA): Part II: 1998  2000 ("PrincetonBarcelonaGdansk")
, 2003
"... This article is a continuation of our previous Algorithmic Column [54] (EATCS, 77, 2002) dedicated to activities of the Analysis of Algorithms group during the \Dagstuhl{ Period" (19931997). The rst three meetings took place in Schloss Dagstuhl, Germany. ..."
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This article is a continuation of our previous Algorithmic Column [54] (EATCS, 77, 2002) dedicated to activities of the Analysis of Algorithms group during the \Dagstuhl{ Period" (19931997). The rst three meetings took place in Schloss Dagstuhl, Germany.
Methodol Comput Appl Probab (2008) 10:507–529 DOI 10.1007/s110090079059x Approximating Perpetuities
, 2007
"... Abstract We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the perpetuity. We significantly reduce the complexity of the e ..."
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Abstract We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the perpetuity. We significantly reduce the complexity of the earlier algorithm. Also one particular perpetuity arising in the analysis of the selection algorithm Quickselect is studied in more detail. Our approach works well for distribution functions. For densities we have weaker error bounds although computer experiments indicate that densities can also be approximated well.
unknown title
, 2008
"... We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the perpetuity. We significantly reduce the complexity of the earlier al ..."
Abstract
 Add to MetaCart
We propose and analyze an algorithm to approximate distribution functions and densities of perpetuities. Our algorithm refines an earlier approach based on iterating discretized versions of the fixed point equation that defines the perpetuity. We significantly reduce the complexity of the earlier algorithm. Also one particular perpetuity arising in the analysis of the selection algorithm Quickselect is studied in more detail. Our approach works well for distribution functions. For densities we have weaker error bounds although computer experiments indicate that densities can also be approximated well.