Gopal K Basak
Articles written in Proceedings – Mathematical Sciences
Volume 115 Issue 4 November 2005 pp 493-498
A functional central limit theorem for a class of urn models
We construct an independent increments Gaussian process associated to a class of multicolor urn models. The construction uses random variables from the urn model which are different from the random variables for which central limit theorems are available in the two color case.
Volume 117 Issue 4 November 2007 pp 517-543
Central Limit Theorems for a Class of Irreducible Multicolor Urn Models
We take a unified approach to central limit theorems for a class of irreducible multicolor urn models with constant replacement matrix. Depending on the eigenvalue, we consider appropriate linear combinations of the number of balls of different colors. Then under appropriate norming the multivariate distribution of the weak limits of these linear combinations is obtained and independence and dependence issues are investigated. Our approach consists of looking at the problem from the viewpoint of recursive equations.
Volume 123 Issue 1 February 2013 pp 85-100
Gopal K Basak Arunangshu Biswas
In this paper we show that the continuous version of the self-normalized process $Y_{n,p}(t)=S_n(t)/V_{n,p}+(nt-[nt])X_{[nt]+1}/V_{n,p},0 < t \leq 1;p>0$ where $S_n(t)=\sum^{[nt]}_{i=1}X_i$ and $V_{(n,p)}=\left(\sum^n_{i=1}|X_i|^p\right)^{1/p}$ and $X_i i.i.d.$ random variables belong to $DA(\alpha)$, has a non-trivial distribution $\mathrm{iff } p=\alpha=2$. The case for $2>p>\alpha$ and $p\leq\alpha < 2$ is systematically eliminated by showing that either of tightness or finite dimensional convergence to a non-degenerate limiting distribution does not hold. This work is an extension of the work by Csörgő
Volume 131, 2021
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