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Invariance properties of the negative binomial Levy process and stochastic self-similarity
International Mathematical Forum
We study the concept of self-similarity with respect to stochastic time change. The negative binomial process (NBP) is an example of a family of random time transformations with respect to which stochastic self-similarity holds for certain stochastic processes. These processes include gamma process, geometric stable processes, Laplace motion, and fractional Laplace motion. We derive invariance properties of the NBP with respect to random time deformations in connection with stochasticdoi:10.12988/imf.2007.07133 fatcat:jni64qwysbdyvpoizerunlao4q