TY - UNPB

T1 - Positive reinforced generalized time-dependent Pólya urns via stochastic approximation

AU - Ruszel, Wioletta

AU - Thacker, Debleena

PY - 2022/1/29

Y1 - 2022/1/29

N2 - Consider a generalized time-dependent Pólya urn process defined as follows. Let d∈N be the number of urns/colors. At each time n, we distribute σn balls randomly to the d urns, proportionally to f, where f is a valid reinforcement function. We consider a general class of positive reinforcement functions R assuming some monotonicity and growth condition. The class R includes convex functions and the classical case f(x)=xα, α>1. The novelty of the paper lies in extending stochastic approximation techniques to the d-dimensional case and proving that eventually the process will fixate at some random urn and the other urns will not receive any balls any more.

AB - Consider a generalized time-dependent Pólya urn process defined as follows. Let d∈N be the number of urns/colors. At each time n, we distribute σn balls randomly to the d urns, proportionally to f, where f is a valid reinforcement function. We consider a general class of positive reinforcement functions R assuming some monotonicity and growth condition. The class R includes convex functions and the classical case f(x)=xα, α>1. The novelty of the paper lies in extending stochastic approximation techniques to the d-dimensional case and proving that eventually the process will fixate at some random urn and the other urns will not receive any balls any more.

U2 - 10.48550/arXiv.2201.12603

DO - 10.48550/arXiv.2201.12603

M3 - Preprint

SP - 1

EP - 22

BT - Positive reinforced generalized time-dependent Pólya urns via stochastic approximation

PB - arXiv

ER -