202 research outputs found
On the product formula on non-compact Grassmannians
We study the absolute continuity of the convolution of two orbital measures on the symmetric space
SO_0(p,q)/SO(p)\timesSO(q), . We prove sharp conditions on , Y\in\a
for the existence of the density of the convolution measure. This measure
intervenes in the product formula for the spherical functions. We show that the
sharp criterion developed for \SO_0(p,q)/\SO(p)\times\SO(q) will also serve
for the spaces SU(p,q)/S(U(p)\timesU(q)) and Sp(p,q)/Sp(p)\timesSp(q),
. We also apply our results to the study of absolute continuity of
convolution powers of an orbital measure
On Wiener-Hopf factors for stable processes
We give a series representation of the logarithm of the bivariate Laplace
exponent of -stable processes for almost all .Comment: 16 pages. to appear in Annales IHP, 201
Riesz measures and Wishart laws associated to quadratic maps
We introduce a natural definition of Riesz measures and Wishart laws
associated to an -positive (virtual) quadratic map, where is a regular open convex cone. We give a general formula for
moments of the Wishart laws. Moreover, if the quadratic map has an equivariance
property under the action of a linear group acting on the cone
transitively, then the associated Riesz measure and Wishart law are described
explicitly by making use of theory of relatively invariant distributions on
homogeneous cones
Convolution of orbital measures on symmetric spaces of type and
We study the absolute continuity of the convolution of two orbital measures on the symmetric spaces
, \SU(p,p)/{\bf S}({\bf
U}(p)\times{\bf U}(p)) and \Sp(p,p)/{\bf Sp }(p)\times\Sp(p). We prove sharp
conditions on , Y\in\a for the existence of the density of the convolution
measure. This measure intervenes in the product formula for the spherical
functions.Comment: arXiv admin note: text overlap with arXiv:1212.000
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
On exit time of stable processes
We study the exit time for 1-dimensional strictly
stable processes and express its Laplace transform at as the Laplace
transform of a positive random variable with explicit density. Consequently,
satisfies some multiplicative convolution relations. For some stable
processes, e.g. for the symmetric -stable process, explicit formulas
for the Laplace transform and the density of are obtained as an
application
Martin representation and Relative Fatou Theorem for fractional Laplacian with a gradient perturbation
Let with . We prove the
Martin representation and the Relative Fatou Theorem for non-negative singular
-harmonic functions on bounded open sets.Comment: 28 pages, editorial change
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