437 research outputs found
Strong solutions of non-colliding particle systems
We study systems of stochastic differential equations describing positions
x_1,x_2,...,x_p of p ordered particles, with inter-particles repulsions of the
form H_{ij}(x_i,x_j)/(x_i-x_j). We show the existence of strong and pathwise
unique non-colliding solutions of the system with a colliding initial point
x_1(0)\leq ...\leq x_p(0) in the whole generality, under natural assumptions on
the coefficients of the equations.Comment: 19 page
Hitting times of Bessel processes
Let be the first hitting time of the point 1 by the Bessel
process with index starting from . Using an integral formula
for the density of , obtained in Byczkowski,
Ryznar (Studia Math., 173(1):19-38, 2006), we prove sharp estimates of the
density of which exibit the dependence both on time and space
variables. Our result provides optimal estimates for the density of the hitting
time of the unit ball by the Brownian motion in , which improve
existing bounds. Another application is to provide sharp estimates for the
Poisson kernel for half-spaces for hyperbolic Brownian motion in real
hyperbolic spaces
Multidimensional Yamada-Watanabe theorem and its applications to particle systems
A multidimensional version of the Yamada-Watanabe theorem is proved. It
implies a spectral matrix Yamada-Watanabe theorem. It is also applied to
particle systems of squared Bessel processes, corresponding to matrix analogues
of squared Bessel processes: Wishart and Jacobi matrix processes. The
beta-versions of these particle systems are also considered.Comment: 16 page
- …