An operational calculus for matrix-exponential distributions, with applications to a Brownian (q, Q) inventory model
成果类型：
Article
署名作者：
Asmussen, S; Perry, D
署名单位：
Lund University; University of Haifa
刊物名称：
MATHEMATICS OF OPERATIONS RESEARCH
ISSN/ISSBN：
0364-765X
DOI：
10.1287/moor.23.1.166
发表日期：
1998
页码：
166-176
关键词：
摘要：
A distribution G on (0, infinity) is called matrix-exponential if the density has the form alpha e(Tz)s where tu is a row vector, T a square matrix and s a column vector. Equivalently, the Laplace transform is rational. For such distributions, we develop an operator calculus, where the key step is manipulation of analytic functions f(z) extended to matrix arguments. The technique is illustrated via an inventory model moving according to a reflected Brownian motion with negative drift, such that an order of size Q is placed when the stock process down-crosses some level q. Explicit formulas for the stationary density are found under the assumption that the leadtime Z has a matrix-exponential distribution, and involve expressions of the form f(T) where f(z) = root 1-2z.