Poisson Limit for Associated Random Fields
Yuri Bakhtin
TL;DR
This paper proves that under certain conditions, associated random fields, when rescaled, converge to a Poisson Point Process, with examples illustrating the result.
Contribution
It establishes a general convergence result for associated random fields to the Poisson process under verifiable conditions.
Findings
Convergence of associated random fields to Poisson process
Provides verifiable conditions for convergence
Includes illustrative examples
Abstract
We prove that under an easily verifiable set of conditions a sequence of associated random fields converges under rescaling to the Poisson Point Process and give a couple of examples.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Probability and Risk Models · Stochastic processes and financial applications