Abstract
In this paper, we define a tempered space fractional negative binomial process (TSFNBP) by replacing the Poisson process by a tempered space fractional Poisson process (TSFPP) in the gamma subordinated form of the negative binomial process. We studied its distributional properties, long-range dependence (LRD) property and its connection with pde’s. The LRD property for the TSFPP process is also investigated. Finally, we present simulated sample paths for both the TSFPP and the TSFNBP.
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