Let be the space of real cadlag functions on with finite limits at ±[infinity], equipped with uniform distance, and let Xn be the empirical process for an exchangeable sequence of random variables. If regarded as a random element of , Xn can fail to converge in distribution. However, in this...

Perfect simulation of an one-dimensional loss network on with length distribution [pi] and cable capacity C can be performed using the clan of ancestors method. Domination of the clan of ancestors by a branching process with dependency in two generations improves the known sufficient conditions...

The correct valuation of the so-called "correlation products" in the credit risk market such as n-th-to-default swaps or CDOs requires a better understanding of higher dimensional barrier default phenomena. We introduce a reflection principle suited for the pricing of credit derivatives on two...

We consider Galton-Watson trees associated with a critical offspring distribution and conditioned to have exactly n vertices. These trees are embedded in the real line by assigning spatial positions to the vertices, in such a way that the increments of the spatial positions along edges of the...

We study a non-Gaussian and non-stable process arising as the limit of sums of rescaled renewal processes under the condition of intermediate growth. The process has been characterized earlier by the cumulant generating function of its finite-dimensional distributions. Here, we derive a more...

Consider events of the form {Zs=[zeta](s),s[set membership, variant]S}, where Z is a continuous Gaussian process with stationary increments, [zeta] is a function that belongs to the reproducing kernel Hilbert space R of process Z, and is compact. The main problem considered in this paper is...

The proportional hazards regression model, when subjects enter the study in a staggered fashion, is studied. A strong martingale approach is used to model the two-time parameter counting processes. It is shown that well-known univariate results such as weak convergence and martingale...

Let be a d-dimensional random walk in random scenery, i.e., with a random walk in and an i.i.d. scenery, independent of the walk. We assume that the random variables Yz have a stretched exponential tail. In particular, they do not possess exponential moments. We identify the speed and the rate...

For S a subordinator and [Pi]n an independent Poisson process of intensity we are interested in the number Kn of gaps in the range of S that are hit by at least one point of [Pi]n. Extending previous studies in [A.V. Gnedin, The Bernoulli sieve, Bernoulli 10 (2004) 79-96; A.V. Gnedin, J. Pitman,...

A scenery is a coloring [xi] of the integers. Let (S(t))t=0 be a recurrent random walk on the integers. Observing the scenery [xi] along the path of this random walk, one sees the color [xi](S(t)) at time t. The scenery reconstruction problem is concerned with trying to retrieve the scenery...