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Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics ha...
In this paper, we shall be concerned with geometric functionals and excursion probabilities for some nonlinear transforms evaluated on Fourier components of spherical random fields. In particular, we ...
Using methods analogous to those introduced in Doney (2005),we express the resolvent density of a(killed)reflected Levy prcess in terms of the resolvent density of the (killed)Levy process. As an appl...
The Brownian excursion measure is a conformally invariant innite measure on curves. It gured prominently in one of rst major applications of SLE, namely the explicit calculations of the planar Brownia...
This survey is a collection of various results and formulas by different authors on the areas (integrals) of five related processes, viz. Brownian motion, bridge, excursion, meander and double meander...
The law for the time tau_{a} spent by a standard Brownian excursion above a given level a>0 is found using Ito excursion theory. This is achieved by conditioning the excursion to have exactly one mark...
For a function $ell$ satisfying suitable integrability (but not continuity) requirements, we construct a process $(B^ell_u, 0 leq u leq 1)$ interpretable as Brownian excursion conditioned to have loca...
In this note we prove strong invariance principles between ranked excursion lengths and heights of a simple random walk and those of a standard Brownian motion. Some consequences concerning limiting d...

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