Let be a two-parameter semimartingale, where M is a continuous martingale, [Lambda] is the character of the Poisson point measure Y, N=Y-[Lambda], we prove that f(Xz) is expressible as such a sum once again via the partial differentiation formula, where f is a twice continuously differentiable...

A necessary and sufficient condition is given for the convergence in probability of a stochastic process {Xt}. Moreover, as a byproduct, an almost sure convergent stochastic process {Yt} with the same limit as {Xt} is identified. In a number of cases {Yt} reduces to {Xt} thereby proving a.s....

We define a general Wiener disorder problem in which a sudden change in a time profile of unknown size has to be detected in white noise of small intensity. Since both the time of the change and its size are unknown, this problem is considerably harder than standard Wiener disorder problems...

Motivated by Barron (1986, Ann. Probab. 14, 336-342), Brown (1982, Statistics and Probability: Essays in Honour of C.R. Rao, pp. 141-148) and Carlen and Soffer (1991, Comm. Math. Phys. 140, 339-371), we prove a version of the Lindeberg-Feller Theorem, showing normal convergence of the normalised...

We study a stochastic flow of -homeomorphisms of . At certain stopping times, the spatial derivative of the flow is a diffusion in the space variable and its generator is given. This answers several questions posed in a previous study by Bass and Burdzy (1999, Ann. Probab. 27, 50-108).

We introduce the concept of capacitary modulus for a set , which is a function h that provides simple estimates for the capacity of [Lambda] with respect to an arbitrary kernel f, estimates which depend only on the L2 inner product (h,f). We show that for a large class of Lévy processes, which...

This paper investigates the behaviour of the random walk Metropolis algorithm in high-dimensional problems. Here we concentrate on the case where the components in the target density is a spatially homogeneous Gibbs distribution with finite range. The performance of the algorithm is strongly...

This paper studies the equivalence of exponential ergodicity and L2-exponential convergence mainly for continuous-time Markov chains. In the reversible case, we show that the known criteria for exponential ergodicity are also criteria for L2-exponential convergence. Until now, no criterion for...

We consider the embedding of a probability distribution in Brownian motion with drift. We first give a sufficient condition on the target measure, under which a variant of the Azéma-Yor (1979a, Séminaire de Probabilités XIII, Lecture Notes in Mathematics, Vol. 721, Springer, Berlin, pp....

Let {Xi: i[greater-or-equal, slanted]1} be i.i.d. uniform points on [-1/2,1/2]d, d[greater-or-equal, slanted]2, and for 0p[infinity]. Let L({X1,...,Xn},p) be the total weight of the minimal spanning tree on {X1,...,Xn} with weight function w(e)=ep. Then, there exist strictly positive but finite...