Results 1  10
of
12
Laplace operators on differential forms over configuration spaces
 J. Geom. Phys
"... Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on forms and associated semigroups are considered. Their probabilistic interpretation is given. 2000 AMS Mathematics Subject Classification. 60G57, ..."
Abstract

Cited by 9 (5 self)
 Add to MetaCart
(Show Context)
Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on forms and associated semigroups are considered. Their probabilistic interpretation is given. 2000 AMS Mathematics Subject Classification. 60G57, 58A10Contents
de Rham cohomology of configuration spaces with Poisson measure
 J. Funct. Anal
, 1995
"... The space ΓX of all locally finite configurations in a Riemannian manifold X of infinite volume is considered. The deRham complex of squareintegrable differential forms over ΓX, equipped with the Poisson measure, and the corresponding deRham cohomology are studied. The latter is shown to be unitari ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
The space ΓX of all locally finite configurations in a Riemannian manifold X of infinite volume is considered. The deRham complex of squareintegrable differential forms over ΓX, equipped with the Poisson measure, and the corresponding deRham cohomology are studied. The latter is shown to be unitarily isomorphic to a certain Hilbert tensor algebra generated by the L 2cohomology of the underlying manifold X.
Laplace operators and diffusions in tangent bundles over Poisson spaces
 Preprint SFB 256 No. 629, Universität
, 1999
"... Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on 1forms and associated semigroups are considered. Their probabilistic interpretation is given. 1 ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
(Show Context)
Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on 1forms and associated semigroups are considered. Their probabilistic interpretation is given. 1
Blowup and stability of semilinear PDE's with gamma generator
, 2004
"... We investigate finitetime blowup and stability of semilinear partial differential equations of the form @w t =@t = w t +t t , w 0 (x) = '(x) 0, x 2 R+ , where is the generator of the standard gamma process and > 0, 2 R, > 0 are constants. We show that any initial value satisf ..."
Abstract

Cited by 5 (4 self)
 Add to MetaCart
We investigate finitetime blowup and stability of semilinear partial differential equations of the form @w t =@t = w t +t t , w 0 (x) = '(x) 0, x 2 R+ , where is the generator of the standard gamma process and > 0, 2 R, > 0 are constants. We show that any initial value satisfying c 1 x '(x), x > x 0 for some positive constants x 0 ; c 1 ; a 1 , yields a nonglobal solution if a 1 < 1 + , or if a 1 = 1 + and > 1. If '(x) c 2 x , x > x 0 ; where x 0 ; c 2 ; a 2 > 0, and a 2 > 1 + , then the solution w t is global and satis es 0 w t (x) Ct , x 0, for some constant C > 0. This extends the results previously obtained in the case of stable generators. Systems of semilinear PDE's with gamma generators are also considered.
Sensitivity analysis and density estimation for finitetime ruin probabilities
 Journal of Computational and Applied Mathematics
"... The goal of this paper is to obtain probabilistic representation formulas that are suitable for the numerical computation of the (possibly noncontinuous) density functions of infima of reserve processes commonly used in insurance. In particular we show, using Monte Carlo simulations, that these rep ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
The goal of this paper is to obtain probabilistic representation formulas that are suitable for the numerical computation of the (possibly noncontinuous) density functions of infima of reserve processes commonly used in insurance. In particular we show, using Monte Carlo simulations, that these representation formulas perform better than standard finite difference methods. Our approach differs from Malliavin probabilistic representation formulas which generally require more smoothness on random variables and entail the continuity of their density functions.
Laplace operators in deRham complexes associated with measures on configuration spaces
, 2001
"... ..."
On local compactness in quasilinear elliptic
"... On local compactness in quasilinear elliptic problems ..."
Critical Exponents for Semilinear PDEs with Bounded Potentials
, 2005
"... Pr'epublications du D'epartement de Math'ematiques ..."
Pr'epublications du D'epartement de Math'ematiques
"... On maximal inequalities for stable stochastic integrals Ald'eric Joulin ..."
Abstract
 Add to MetaCart
On maximal inequalities for stable stochastic integrals Ald'eric Joulin