We study large deviations for Brownian motion on the Sierpinski gasket in the short time limit. Because of the subtle oscillation of hitting times of the process, no large deviation principle can hold. In fact, our result shows that there is an infinity of different large deviation principles...

A Bayesian estimation problem is considered, in which the observation is a vector-valued, continuous-time stochastic process of the 'signal-plus-white-noise' variety and approximations based on sampling and quantisation of this process are developed. The problem includes continuous-time...

Let X1,X2,X3,... be independent d-dimensional variables with common density function f. Let Ri,k,n be the distance from Xi to its kth nearest neighbour in {X1,...,Xn}. Suppose (kn) is a sequence with 1knn2/(2+d) as n tends to infinity (or 1knn2/3 for a uniform distribution). Subject to...

We study the weak approximation of a multidimensional diffusion (Xt)0[less-than-or-equals, slant]t[less-than-or-equals, slant]T killed as it leaves an open set D, when the diffusion is approximated by its continuous Euler scheme or by its discrete one , with discretization step T/N. If we set...

In this paper, we are interested in the one-dimensional porous medium equation when the initial condition is the distribution function of a probability measure. We associate a nonlinear martingale problem with it. After proving uniqueness for the martingale problem, we show existence owing to a...

In this paper the maximum likelihood and quasi-maximum likelihood estimators of a spectral parameter of a mean zero Gaussian stationary process are shown to be asymptotically efficient in the sense of Bahadur under appropriate conditions. In order to obtain exponential convergence rates of tail...

We have given several necessary and sufficient conditions for statistically self-similar sets and a.s. self-similar sets and have got the Hausdorff dimension and exact Hausdorff measure function of any a.s. self-similar set in this paper. It is useful in the study of probability properties and...

A renewal process is called ordinary if its inter-renewal times are strictly positive. S.M. Samuels proved in 1974 that if the superposition of two ordinary renewal processes is an ordinary renewal process, then all processes are Poisson. This result is generalized here to the case of processes...

We define a reinforced urn process (RUP) to be a reinforced random walk on a state space of urns and we show its partial exchangeability. When it is recurrent, a RUP is a mixture of Markov chains and we characterize its mixing distribution on the space of stochastic matrices. Many Bayesian...

We study the equilibrium fluctuations of a tagged particle driven by an external constant force in an infinite system of particles evolving in a one-dimensional lattice according to symmetric random walks with exclusion. We prove that when the system is initially in the equilibrium state, the...