TY  - BOOK
A1  - Dereudre, David
A1  - Roelly, Sylvie
T1  - On Gibbsianness of infinite-dimensional diffusions
N2  - We analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the lattice $Z^{d} : X = (X_{i}(t), i ∈ Z^{d}, t ∈ [0, T], 0 < T < +∞)$. In a first part, these processes are characterized as Gibbs states on path spaces of the form $C([0, T],R)Z^{d}$. In a second part, we study the Gibbsian character on $R^{Z}^{d}$ of $v^{t}$, the law at time t of the infinite-dimensional diffusion X(t), when the initial law $v = v^{0}$ is Gibbsian.
T3  - Mathematische Statistik und Wahrscheinlichkeitstheorie : Preprint - 2004, 01 
KW  - infinite-dimensional Brownian diffusion
KW  - Gibbs field
KW  - cluster expansion
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-52630
ER  - 
TY  - GEN
A1  - Roelly, Sylvie
A1  - Dereudre, David
T1  - On Gibbsianness of infinite-dimensional diffusions
N2  - The authors analyse different Gibbsian properties of interactive Brownian diffusions X indexed by the d-dimensional lattice. In the first part of the paper, these processes are characterized as Gibbs states on path spaces. In the second part of the paper, they study the Gibbsian character on R^{Z^d} of the law at time t of the infinite-dimensional diffusion X(t), when the initial law is Gibbsian.  AMS Classifications: 60G15 , 60G60 , 60H10 , 60J60
KW  - infinite-dimensional Brownian diffusion
KW  - Gibbs field
KW  - cluster expansion
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-6692
ER  -