Pruitt's Estimates in Banach Space
Philip S. Griffin

TL;DR
This paper extends Pruitt's estimates for exit times of random walks to infinite-dimensional Banach spaces, revealing their dependence on space type and cotype, and characterizing these properties.
Contribution
It introduces a novel extension of Pruitt's estimates to infinite-dimensional Banach spaces and characterizes space types based on these estimates.
Findings
Estimates depend on whether the space is type 2 or cotype 2.
These estimates characterize the type and cotype of Banach spaces.
Extension of finite-dimensional results to infinite-dimensional settings.
Abstract
Pruitt's estimates on the expectation and the distribution of the time taken by a random walk to exit a ball of radius r are extended to the infinite dimensional setting. It is shown that they separate into two pairs of estimates depending on whether the space is type 2 or cotype 2. It is further shown that these estimates characterize type 2 and cotype 2 spaces.
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Taxonomy
TopicsProbability and Risk Models · Stochastic processes and financial applications · Stochastic processes and statistical mechanics
