We analyse the quasi-stationary distributions of the family of Markov chains {Xn[var epsilon]},[var epsilon]0, obtained from small non-local random perturbations of iterates of a map f : I--I on a compact interval. The class of maps considered is slightly more general than the class of...

The generalized Friedman's urn (GFU) model has been extensively applied to biostatistics. However, in the literature, all the asymptotic results concerning the GFU are established under the assumption of a homogeneous generating matrix, whereas, in practical applications, the generating matrices...

Given a process X on or , we may form a random sequence [xi]1,[xi]2,... by sampling from X at some independent points [tau]1,[tau]2,... . If X is stationary up to shifts (which holds for broad classes of Markov and Palm processes) and the distribution of ([tau]n) is asymptotically invariant (as...

Mark Kac introduced a method for calculating the distribution of the integral Av=[integral operator]0Tv(Xt) dt for a function v of a Markov process (Xt, t[greater-or-equal, slanted]0) and a suitable random time T, which yields the Feynman-Kac formula for the moment-generating function of Av. We...

We study the nonparametric estimation of the coefficients of a 1-dimensional diffusion process from discrete observations. Different asymptotic frameworks are considered. Minimax rates of convergence are studied over a wide range of Besov smoothness classes. We construct estimators based on...

We are interested in the functional convergence in distribution of the process of quadratic variations taken along a regular partition for a large class of Gaussian processes indexed by [0,1], including the standard Wiener process as a particular case. This result is applied to the estimation of...

We show for the branching Lévy process that it is possible to construct two classes of multiplicative martingales using stopping lines and solutions to one of two source equations. The first class, similar to those martingales of Chauvin (1991, Ann. Probab. 30, 1195-1205) and Neveu (1988,...

Motivated by the Kyle-Back model of "insider trading", we consider certain classes of linear transformations of two independent Brownian motions and study their canonical decomposition, i.e., their Doob-Meyer decomposition as semimartingales in their own filtration. In particular we characterize...

Poisson approximation in total variation can be successfully established in a wide variety of contexts, involving sums of weakly dependent random variables which usually take the value 0, and occasionally the value 1. If the random variables can take other positive integer values, or if there is...

Lerchez (Ann. Statist. 14, 1986b, 1030-1048) considered a sequential Bayes-test problem for the drift of the Wiener process. In the case of a normal prior an o(c)-optimal test could be constructed. In this paper a new martingale approach is presented, which provides an expansion of the Bayes...