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533
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 86 (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
Bivariate Uniqueness and Endogeny for the Logistic Recursive Distributional Equation
, 2008
"... In this article we prove the bivariate uniqueness property for a particular “maxtype ” recursive distributional equation (RDE). Using the general theory developed in [5] we then show that the corresponding recursive tree process (RTP) has no external randomness, more preciously, the RTP is endogeno ..."
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Cited by 2 (0 self)
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In this article we prove the bivariate uniqueness property for a particular “maxtype ” recursive distributional equation (RDE). Using the general theory developed in [5] we then show that the corresponding recursive tree process (RTP) has no external randomness, more preciously, the RTP
c ○ European Mathematical Society Endogeny for the Logistic Recursive Distributional Equation
"... Abstract. In this article we prove the endogeny and bivariate uniqueness property for a particular “maxtype ” recursive distributional equation (RDE). The RDE we consider is the so called logistic RDE, which appears in the proof of the ζ(2)limit of the random assignment problem using the local wea ..."
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Abstract. In this article we prove the endogeny and bivariate uniqueness property for a particular “maxtype ” recursive distributional equation (RDE). The RDE we consider is the so called logistic RDE, which appears in the proof of the ζ(2)limit of the random assignment problem using the local
On stochastic recursive equations of sum and maxtype
 Journal of Applied Probability
, 2006
"... In this paper we consider stochastic recursive equations of sumtype X d = �K i=1 AiXi+b and of maxtype X d = max(AiXi+bi; 1 ≤ i ≤ k) where Ai, bi, b are random and (Xi) are iid copies of X. Equations of this type typically characterize limits in the probabilistic analysis of algorithms, in combinat ..."
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Cited by 3 (2 self)
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In this paper we consider stochastic recursive equations of sumtype X d = �K i=1 AiXi+b and of maxtype X d = max(AiXi+bi; 1 ≤ i ≤ k) where Ai, bi, b are random and (Xi) are iid copies of X. Equations of this type typically characterize limits in the probabilistic analysis of algorithms
TIGHTNESS FOR A FAMILY OF RECURSION EQUATIONS
"... Abstract. In this paper, we study the tightness of solutions for a family of recursion equations. These equations arise naturally in the study of random walks on treelike structures. Examples include the maximal displacement of branching random walk in one dimension, and the cover time of symmetric ..."
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Cited by 31 (6 self)
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of symmetric simple random walk on regular binary trees. Recursion equations associated with the distribution functions of these quantities have been used to establish weak laws of large numbers. Here, we use these recursion equations to establish the tightness of the corresponding sequences of distribution
Distributive laws for the coinductive solution of recursive equations
 Information and Computation
"... This paper illustrates the relevance of distributive laws for the solution of recursive equations, and shows that one approach for obtaining coinductive solutions of equations via infinite terms is in fact a special case of a more general approach using an extended form of coinduction via distributi ..."
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Cited by 23 (1 self)
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This paper illustrates the relevance of distributive laws for the solution of recursive equations, and shows that one approach for obtaining coinductive solutions of equations via infinite terms is in fact a special case of a more general approach using an extended form of coinduction via
Bivariate Uniqueness in the Logistic Recursive Distributional Equation
, 2002
"... In this work we prove the bivariate uniqueness property of the Logistic fixedpoint equation, which arise in the study of the random assignment problem, as discussed by Aldous [4]. Using this and the general framework of Aldous and Bandyopadhyay [2], we then conclude that the associated recursive tr ..."
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Cited by 4 (1 self)
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In this work we prove the bivariate uniqueness property of the Logistic fixedpoint equation, which arise in the study of the random assignment problem, as discussed by Aldous [4]. Using this and the general framework of Aldous and Bandyopadhyay [2], we then conclude that the associated recursive
RECURSIVE FORMULAS FOR COMPOUND DIFFERENCE DISTRIBUTIONS*
"... Recursive formulas satisfied by the numbers of claims are lifted to recursire formulas satisfied by the amounts of aggregate claims. The derivation relies on only an elementary techniquepower series solutions to differential equations. The formulas are useful in the application of risk theory and ..."
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Recursive formulas satisfied by the numbers of claims are lifted to recursire formulas satisfied by the amounts of aggregate claims. The derivation relies on only an elementary techniquepower series solutions to differential equations. The formulas are useful in the application of risk theory
Estimating Fully Observed Recursive MixedProcess Models with cmp,” Working Papers 168
, 2009
"... At the heart of many econometric models is a linear function and a normal error. Examples include the classical smallsample linear regression model and the probit, ordered probit, multinomial probit, Tobit, interval regression, and truncateddistribution regression models. Because the normal distri ..."
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Cited by 86 (2 self)
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facilitates a generalization to switching, selection, and other models in which the number and types of equations vary by observation. The Stata module cmp fits Seemingly Unrelated Regressions (SUR) models of this broad family. Its estimator is also consistent for recursive systems in which all endogenous
On the stability of recursive formulas
 ASTIN Bulletin
, 1993
"... Based on recurrence quation theory and relative error (rather than absolute error) analysis, the concept and criterion for the stability of a recurrence equation are clarified. A family of recursions, called congruent recursions, is proved to be strongly stable in evaluating its nonnegative solutio ..."
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Cited by 19 (0 self)
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negative solutions. A type of strongly unstable recursion is identified. The recursive formula discussed by PANJER (1981) is proved to be strongly stable in evaluating the compound Poisson and the compound Negative Binomial (including Geometric) distributions. For the compound Binomial distribution, the recursion
Results 1  10
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533