31 citations · 121 across the 16 of their papers we have counts for
18 papers
The Test and Find Model
Michael Grabchak, Xingjie Li, Isaac M. Sonin
We introduce the Test and Find (TF) problem, where a decision maker (DM) faces the following situation: identical objects are randomly allocated to distinct boxes (sites) a…
On the Simulation of General Multivariate Gamma Distributions using Dickman Approximations
Michael Grabchak, Xingnan Zhang
We derive a Dickman approximation for the small jumps of a large class of multivariate Lévy processes. We then apply this approximation to develop a simulation method for the class…
Representation and Simulation of Multivariate Dickman Distributions and Vervaat Perpetuities
Michael Grabchak, Xingnan Zhang
A multivariate extension of the Dickman distribution was recently introduced, but very few properties have been studied. We discuss several properties with an emphasis on simulatio…
Efficient Simulation of -Tempered -Stable OU Processes
Michael Grabchak, Piergiacomo Sabino
We develop efficient methods for simulating processes of Ornstein-Uhlenbeck type related to the class of -tempered -stable ($\ts$) distributions. Our results hold for both th…
A Zero-One Law for Markov Chains
Michael Grabchak, Isaac Sonin
We prove an analog of the classical Zero-One Law for both homogeneous and nonhomogeneous Markov chains (MC). Its almost precise formulation is simple: given any event from the…
An Exact Method For Simulating Rapidly Decreasing Tempered Stable Distributions
Michael Grabchak
Rapidly decreasing tempered stable distributions are useful models for financial applications. However, there has been no exact method for simulation available in the literature. W…
On the Transition Laws of -Tempered -Stable OU-Processes
Michael Grabchak
We derive an explicit representation for the transition law of a -tempered -stable process of Ornstein-Uhlenbeck-type and use it to develop a methodology for simulation. Our…
On the Simulation of General Tempered Stable Ornstein-Uhlenbeck Processes
Michael Grabchak
We give an explicit representation for the transition law of a tempered stable Ornstein-Uhlenbeck process and use it to develop a rejection sampling algorithm for exact simulation…
On the occupancy problem for a regime switching model
Michael Grabchak, Mark Kelbert, Quentin Paris
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distribute…
Rejection Sampling for Tempered Levy Processes
Michael Grabchak
We extend the idea of tempering stable Levy processes to tempering more general classes of Levy processes. We show that the original process can be decomposed into the sum of the t…
Domains of Attraction for Positive and Discrete Tempered Stable Distributions
Michael Grabchak
We introduce a large and flexible class of discrete tempered stable distributions, and analyze the domains of attraction for both this class and the related class of positive tempe…
Finite sample properties of the mean occupancy counts and probabilities
Geoffrey Decrouez, Michael Grabchak, Quentin Paris
For a probability distribution on an at most countable alphabet , this article gives finite sample bounds for the expected occupancy counts and…
Three Upsilon Transforms Related to Tempered Stable Distributions
Michael Grabchak
We discuss the properties of three upsilon transforms, which are related to the class of -tempered -stable () distributions. In particular, we characterize their doma…
Entropic Representation and Estimation of Diversity Indices
Zhiyi Zhang, Michael Grabchak
This paper serves a twofold purpose. First, a unified perspective on diversity indices is introduced based on an entropic basis. It is shown that the class of all linear combinatio…
A Note on the Multivariate CLT and Convergence of Levy Processes at Long and Short Times
Michael Grabchak
We show that a necessary and sufficient condition for the sum of iid random vectors to converge (under appropriate shifting and scaling) to a multivariate Gaussian distribution is…
Inversions of Levy Measures and the Relation Between Long and Short Time Behavior of Levy Processes
Michael Grabchak
The inversion of a Levy measure was first introduced (under a different name) in Sato 2007. We generalize the definition and give some properties. We then use inversions to derive…
Limit Theorems For Sequences of Tempered Stable and Related Distributions
Michael Grabchak
In this paper we define the closure under weak convergence of the class of p-tempered α-stable distributions. We give necessary and sufficient conditions for convergence of sequenc…
On A New Class of Tempered Stable Distributions: Moments and Regular Variation
Michael Grabchak
We extend the class of tempered stable distributions first introduced in Rosinski 2007. Our new class allows for more structure and more variety of tail behaviors. We discuss vario…