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Mathematical expectation and Strong Law of Large Numbers for random variables with values in a metric space of negative curvature
Mathematical expectation Strong Law of Large Numbers random variables
2009/9/23
Let f be a random variable with values in a metric
space (X, d). For some class of metric spaces we define in terms of the
metric d mathematical expectation of f as a closed bounded and
non-empty s...
Estimates for the Poisson kernels on homogeneous manifolds of negative curvature and the boundary Harnack inequality in the noncoercive case
Estimates for the Poisson kernels homogeneous manifolds negative curvature the boundary Harnack inequality
2009/9/21
Using a probabilistic technique we obtain upper and
lower estimates for the Poisson kernels of the second order diflerential
operators on a homogeneous manifold of negative curvature. Our
results i...
A remark on the Poisson kernels on homogeneous manifolds of negative curvature
Poisson kernels homogeneous manifolds negative curvature
2009/9/21
In this note we give an improvement of the estimate of
the Poisson kernels for second order differential operators on homogeneous
manifolds of negative curvature obtained for the first time,
using ...