Raúl Gouet

A martingale approach to strong convergence in a generalized Pólya-Eggenberger urn model

We obtain strong convergence for the proportion Wn/Tn of white balls in a generalized Polya--Eggenberger urn scheme. We use straightforward martingale arguments that do not require moment estimations.

Strong convergence of proportions in a multicolor Pólya urn

We prove strong convergence of the proportions U n / T n of balls in a multitype generalized Polya urn model, using martingale arguments. The limit is characterized as a convex combination of left dominant eigenvectors of the replacement matrix R, with random Dirichlet coefficients.

Asymptotic normality for the counting process of weak records and δ-records in discrete models

Let

Extrapolation of Urn Models via Poissonization: Accurate Measurements of the Microbial Unknown

\{X_n,n\ge1\}

Central limit theorems for the number of records in discrete models

be a sequence of independent and identically distributed random variables, taking non-negative integer values, and call

A martingale approach to strong convergence of the number of records

X_n

Records from stationary observations subject to a random trend

a

Central Limit Theorem for the Number of Near-Records

\delta

Limit Theorems for the Counting Process of Near-Records

-record if

Statistical inference for the geometric distribution based on δ-records

X_n>\max\{X_1,...,X_{n-1}\}+\delta