Outputs (3)

Positive Reinforced Generalized Time-Dependent Pólya Urns via Stochastic Approximation (2024)
Journal Article
Ruszel, W. M., & Thacker, D. (2024). Positive Reinforced Generalized Time-Dependent Pólya Urns via Stochastic Approximation. Journal of Theoretical Probability, 37(4), 2859-2885. https://doi.org/10.1007/s10959-024-01366-w

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 con... Read More about Positive Reinforced Generalized Time-Dependent Pólya Urns via Stochastic Approximation.

Continuous-time digital search tree and a border aggregation model (2022)
Journal Article
Janson, S., & Thacker, D. (2022). Continuous-time digital search tree and a border aggregation model. Bernoulli (Andover), 28(4), 2563-2577. https://doi.org/10.3150/21-bej1429

We consider the continuous-time version of the random digital search tree, and construct a coupling with a border aggregation model as studied in Thacker and Volkov (Ann. Appl. Probab. 28 (2018) 1604–1633), showing a relation between the height of th... Read More about Continuous-time digital search tree and a border aggregation model.

A new approach to Pólya urn schemes and its infinite color generalization (2022)
Journal Article
Bandyopadhyay, A., & Thacker, D. (2022). A new approach to Pólya urn schemes and its infinite color generalization. Annals of Applied Probability, 32(1), 46-79. https://doi.org/10.1214/21-aap1671

In this work, we introduce a generalization of the classical Pólya urn scheme (Ann. Inst. Henri Poincaré 1 (1930) 117–161) with colors indexed by a Polish space, say, S. The urns are defined as finite measures on S endowed with the Borel σ-algebra, s... Read More about A new approach to Pólya urn schemes and its infinite color generalization.