|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'501'711
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Equilibrium diffusion on the cone of discrete Radon measures | | Diana Conache
; Yuri G. Kondratiev
; Eugene Lytvynov
; | | Date: |
13 Mar 2015 | | Abstract: | Let $mathbb K(mathbb R^d)$ denote the cone of discrete Radon measures on
$mathbb R^d$. There is a natural differentiation on $mathbb K(mathbb R^d)$:
for a differentiable function $F:mathbb K(mathbb R^d) omathbb R$, one
defines its gradient $
abla^{mathbb K} F $ as a vector field which assigns to
each $etain mathbb K(mathbb R^d)$ an element of a tangent space
$T_eta(mathbb K(mathbb R^d))$ to $mathbb K(mathbb R^d)$ at point $eta$.
Let $phi:mathbb R^d imesmathbb R^d omathbb R$ be a potential of pair
interaction, and let $mu$ be a corresponding Gibbs perturbation of (the
distribution of) a completely random measure on $mathbb R^d$. In particular,
$mu$ is a probability measure on $mathbb K(mathbb R^d)$ such that the set of
atoms of a discrete measure $etainmathbb K(mathbb R^d)$ is $mu$-a.s.
dense in $mathbb R^d$. We consider the corresponding Dirichlet form $$
mathscr E^{mathbb K}(F,G)=int_{mathbb K(mathbb R^d)}langle
abla^{mathbb
K} F(eta),
abla^{mathbb K} G(eta)
angle_{T_eta(mathbb K)},dmu(eta).
$$ Integrating by parts with respect to the measure $mu$, we explicitly find
the generator of this Dirichlet form. By using the theory of Dirichlet forms,
we prove the main result of the paper: If $dge2$, there exists a conservative
diffusion process on $mathbb K(mathbb R^d)$ which is properly associated with
the Dirichlet form $mathscr E^{mathbb K}$. | | Source: | arXiv, 1503.4166 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER