BACKGROUND:Giardia is the most frequently identified intestinal parasite in North America. Although information on geographical distribution of giardiasis is critical in identifying communities at high risk, little has been done in this area. Therefore, the objective of this study was…

Using the techniques of the stochastic calculus of variations for Gaussian processes, we derive an It^{o} formula for the fractional Brownian sheet with Hurst parameters bigger than $1/2$. As an application, we give a stochastic integral representation for the local…

We consider in this paper the support $[L',R']$ of the one dimensional Integrated Super Brownian Excursion. We determine the distribution of $(R',L')$ through a modified Laplace transform. Then we give an explicit value for the first two moments of $R'$…

We consider a nearest-neighbor stochastic process on a rooted tree $G$ which goes toward the root with probability $1-\varepsilon$ when it visits a vertex for the first time. At all other times it behaves like a simple random walk on…

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A closed formula for the mean of a maximum likelihood estimator associated with the Brownian bridge is obtained; the exact relation with that of the Brownian motion is established.

We explore planar random walk conditioned to avoid its past convex hull. We prove that it escapes at a positive lim sup speed. Experimental results show that fluctuations from a limiting direction are on the order of $n^{3/4}$. This behavior…

By analogy with Carleson's observation on Cardy's formula describing crossing probabilities for the scaling limit of critical percolation, we exhibit ``privileged geometries'' for Stochastic Loewner Evolutions with various parameters, for which certain hitting distributions are uniformly distributed. We then examine…

The purpose of the present paper is to study the asymptotic behaviour of the products of random matrices indexed by a random walk following the results obtained by Furstenberg and Kesten (MR53:14670) and by Ishitani (MR 53:14670).