9,607 research outputs found
Limit distribution of degrees in random family trees
In a one-parameter model for evolution of random trees, which also includes
the Barabasi-Albert random tree, almost sure behavior and the limiting
distribution of the degree of a vertex in a fixed position are examined.
Results about Polya urn models are applied in the proofs
Limit Distribution of Evolving Strategies in Financial Markets
In this paper we model a financial market composed of agents with heterogeneous beliefs who change their strategy over time. We propose two different solution methods which lead to two different types of endogenous dynamics. The first makes use of the maximum entropy approach to obtain an exponential type probability function for strategies, analogous to the well known Brock and Hommes (1997) model, but with the endogenous specification for the intensity of choice parameter, which varies over time as a consequence of the relative performances of each strategy. The second type of dynamics is obtained by setting up a master equation and solving it using recently developed asymptotic solution techniques, which yield a system of differential equations describing the evolution of the share of each strategy in the market. The performance sof the two solutions are then compared and contrasted with the empirical evidence.
Limit Distribution of Convex-Hull Estimators of Boundaries
Given n independent and identically distributed observations in a set G with an unknown function g, called a boundary or frontier, it is desired to estimate g from the observations. The problem has several important applications including classification and cluster analysis, and is closely related to edge estimation in image reconstruction. It is particularly important in econometrics. The convex-hull estimator of a boundary or frontier is very popular in econometrics, where it is a cornerstone of a method known as `data envelope analysis´ or DEA. In this paper we give a large sample approximation of the distribution of the convex-hull estimator in the general case where p>=1. We discuss ways of using the large sample approximation to correct the bias of the convex-hull and the DEA estimators and to construct confidence intervals for the true function. --Convex-hull,free disposal hull,frontier function,data envelope analysis,productivity analysis,rate of convergence
Stochastic ranking process with time dependent intensities
We consider the stochastic ranking process with the jump times of the
particles determined by Poisson random measures. We prove that the joint
empirical distribution of scaled position and intensity measure converges
almost surely in the infinite particle limit. We give an explicit formula for
the limit distribution and show that the limit distribution function is a
unique global classical solution to an initial value problem for a system of a
first order non-linear partial differential equations with time dependent
coefficients
On the location of the zero-free half-plane of a random Epstein zeta function
In this note we study, for a random lattice L of large dimension n, the
supremum of the real parts of the zeros of the Epstein zeta function E_n(L,s)
and prove that this random variable has a limit distribution, which we give
explicitly. This limit distribution is studied in some detail; in particular we
give an explicit formula for its distribution function.Comment: To appear in Mathematische Annalen. The final publication is
available at https://link.springer.com/article/10.1007/s00208-017-1589-
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