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Self-stabilizing processes

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Abstract We construct “self-stabilizing” processes . These are random processes which when “localized,” that is scaled around t to a fine limit, have the distribution of an -stable process, where… Click to show full abstract

Abstract We construct “self-stabilizing” processes . These are random processes which when “localized,” that is scaled around t to a fine limit, have the distribution of an -stable process, where α is some given function on . Thus the stability index at t depends on the value of the process at t. Here, we address the case where . We first construct deterministic functions which satisfy a kind of autoregressive property involving sums over a plane point set Π. Taking Π to be a Poisson point process then defines a random pure jump process, which we show has the desired localized distributions.

Keywords: self stabilizing; process; stabilizing processes

Journal Title: Stochastic Models
Year Published: 2018

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