Two Types of RG-Factorizations of Continuous-Time Level-Dependent Quasi-Birth-and-Death Processes and Their Applications to Stochastic Integral Functionals
نویسندگان
چکیده
In this paper, we provide UL-type and LU -type RG-factorizations for an irreducible continuous-time level-dependent quasi-birth-and-death (QBD) process with either finitely-many levels or infinitely-many levels, and then apply theRG-factorizations to solve a type of linear QBD-equations, which is always crucial for analyzing a stochastic model described as a QBD process. Based on the results obtained for the linear QBD-equations, we analyze up-, downand return-integral functionals. We explicitly express the Laplace transforms of the conditional distributions of the three types of stochastic integral functionals and their conditional moments.
منابع مشابه
Birth-death processes
Integral functionals of Markov processes are widely used in stochastic modeling for applications in ecology, evolution, infectious disease epidemiology, and operations research. The integral of a stochastic process is often called the “cost” or “reward” accrued by the process. Many important stochastic counting models can be written as general birth-death processes (BDPs), which are continuous-...
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