Phase-type distributions and perturbation model
Pitman's theorem for skip-free random walks with Markovian increments.
Pricing bonds and CDS in the model with rating migration induced by a Cox process
We investigate the properties of a rating migration process assuming that it is given by subordination of a discrete time Markov chain and a Cox process. The problem of pricing of defaultable bonds with fractional recovery of par value with rating migration and credit default swaps is considered. As an example of applications of our results, we give an explicit solution to the pricing problem in a model with short rate and intensity processes given by the solution of a two-dimensional Ornstein-Uhlenbeck...
Prognosis and optimization of homogeneous Markov message handling networks
Message handling systems with finitely many servers are mathematically described as homogeneous Markov networks. For hierarchic networks is found a recursive algorithm evaluating after finitely many steps all steady state parameters. Applications to optimization of the system design and management are discussed, as well as a program product 5P (Program for Prognosis of Performance Parameters and Problems) based on the presented theoretical conclusions. The theoretic achievements as well as the practical...
Propriétés de mélange des processus autorégressifs polynomiaux
Pruning Galton–Watson trees and tree-valued Markov processes
We present a new pruning procedure on discrete trees by adding marks on the nodes of trees. This procedure allows us to construct and study a tree-valued Markov process by pruning Galton–Watson trees and an analogous process by pruning a critical or subcritical Galton–Watson tree conditioned to be infinite. Under a mild condition on offspring distributions, we show that the process run until its ascension time has a representation in terms of . A similar result was obtained by Aldous and...