217 citations · 502 across the 43 of their papers we have counts for
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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…
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…
Binomial Approximation to Locally Dependent CDO
Amit N. Kumar, P. Vellaisamy
In this paper, we develop Stein's method for binomial approximation using the stop-loss metric that allows one to obtain a bound on the error term between the expectation of call f…
Poisson Approximation to the Convolution of Power Series Distributions
A. N. Kumar, P. Vellaisamy, F. Viens
In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method. This provides a unif…