4 papers
A New Compound Poisson Process and Its Fractional Versions
Palaniappan Vellaisamy, Tomoyuki Ichiba
We consider a weighted sum of a series of independent Poisson random variables and show that it results in a new compound Poisson distribution which includes the Poisson distributi…
Bilateral Gamma Approximation in Weiner Space
Kalyan Barman, Tomoyuki Ichiba, Palaniappan Vellaisamy
This paper deals with bilateral-gamma (BG) approximation to functionals of an isonormal Gaussian process. We use Malliavin-Stein method to obtain the error bounds for the smooth Wa…
Approximations Related to Tempered Stable Distributions
Kalyan Burman, Neelesh S Upadhye, Palaniappan Vellaisamy
In this article, we first obtain, for the Kolmogorov distance, an error bound between a tempered stable and a compound Poisson distribution and also an error bound between a temper…
Covariance Identities and Variance Bounds for Infinitely Divisible Random Variables and Their Applications
Kalyan Barman, Neelesh S Upadhye, Palaniappan Vellaisamy
In this article, we establish a general covariance identity for infinitely divisible distributions (IDD). Using this result, we derive Cacoullos type variance bounds for the IDD. A…