Perturbed and non-perturbed brownian taboo processes
Poisson Approximation for the Number of Large Digits of Inhomogeneous f-Expansions.
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...
Problem of uniqueness in the renewal process generated by the uniform distribution.
Quasi-stationary distributions and the continuous-state branching process conditioned to be never extinct.
Random discrete distributions derived from self-similar random sets.
Regenerative renewal processes
Renewal convergence rates and correlation decay for homogeneous pinning models.
Renewal Processes of Mittag-Leffler and Wright Type
2000 MSC: 26A33, 33E12, 33E20, 44A10, 44A35, 60G50, 60J05, 60K05.After sketching the basic principles of renewal theory we discuss the classical Poisson process and offer two other processes, namely the renewal process of Mittag-Leffler type and the renewal process of Wright type, so named by us because special functions of Mittag-Leffler and of Wright type appear in the definition of the relevant waiting times. We compare these three processes with each other, furthermore consider corresponding...
Renewal property of the extrema and tree property of the excursion of a one-dimensional brownian motion
Renewal theorem and Markov chains
Renewal theorems for linear discrete Volterra equations.
Renewal theorems for random walks in multidimensional time
Renewal theory in dimensions II
Ruin models with investment income.
Sharp asymptotic behavior for wetting models in -dimension.
Small and large time stability of the time taken for a Lévy process to cross curved boundaries
This paper is concerned with the small time behaviour of a Lévy process . In particular, we investigate thestabilitiesof the times, and , at which , started with , first leaves the space-time regions (one-sided exit), or (two-sided exit), , as . Thus essentially we determine whether or not these passage times behave like deterministic functions in the sense of different modes of convergence; specifically convergence in probability, almost surely and in . In many instances these are...
Stability in some rarefaction models
Stochastic Behaviour of a Robot-Safety Device System
Sur une généralisation du concept de promenade aléatoire sur la droite réelle