Infinite system of Brownian balls with interaction: the non-reversible case
ESAIM: Probability and Statistics (2007)
- Volume: 11, page 55-79
- ISSN: 1292-8100
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topFradon, Myriam, and Rœlly, Sylvie. "Infinite system of Brownian balls with interaction: the non-reversible case." ESAIM: Probability and Statistics 11 (2007): 55-79. <http://eudml.org/doc/250111>.
@article{Fradon2007,
abstract = {
We consider an infinite system of hard balls in $\xR^d$ undergoing Brownian motions
and submitted to a smooth pair potential.
It is modelized by an infinite-dimensional stochastic differential equation
with an infinite-dimensional local time term.
Existence and uniqueness of a strong solution is proven for such an equation
with fixed deterministic initial condition. We also show
that Gibbs measures are reversible measures.
},
author = {Fradon, Myriam, Rœlly, Sylvie},
journal = {ESAIM: Probability and Statistics},
keywords = {Stochastic differential equation; local time; hard core potential;
Gibbs measure; reversible measure.; stochastic differential equation; Gibbs measure; reversible measure},
language = {eng},
month = {3},
pages = {55-79},
publisher = {EDP Sciences},
title = {Infinite system of Brownian balls with interaction: the non-reversible case},
url = {http://eudml.org/doc/250111},
volume = {11},
year = {2007},
}
TY - JOUR
AU - Fradon, Myriam
AU - Rœlly, Sylvie
TI - Infinite system of Brownian balls with interaction: the non-reversible case
JO - ESAIM: Probability and Statistics
DA - 2007/3//
PB - EDP Sciences
VL - 11
SP - 55
EP - 79
AB -
We consider an infinite system of hard balls in $\xR^d$ undergoing Brownian motions
and submitted to a smooth pair potential.
It is modelized by an infinite-dimensional stochastic differential equation
with an infinite-dimensional local time term.
Existence and uniqueness of a strong solution is proven for such an equation
with fixed deterministic initial condition. We also show
that Gibbs measures are reversible measures.
LA - eng
KW - Stochastic differential equation; local time; hard core potential;
Gibbs measure; reversible measure.; stochastic differential equation; Gibbs measure; reversible measure
UR - http://eudml.org/doc/250111
ER -
References
top- R.L. Dobrushin, Gibbsian random fields. The general case. Functional Anal. Appl.3 (1969) 22–28.
- M. Fradon and S. Rœlly, Infinite dimensional diffusion processes with singular interaction. Bull. Sci. math. 124 (2000) 287–318.
- J. Fritz, Gradient Dynamics of Infinite Points Systems. Ann Probab.15 (1987) 478–514.
- H.-O. Georgii, Canonical Gibbs measures. Lecture Notes in Mathematics 760, Springer-Verlag, Berlin (1979).
- R. Lang, Unendlich-dimensionale Wienerprozesse mit Wechselwirkung. Z. Wahrsch. Verw. Geb.38 (1977) 55–72.
- D. Ruelle, Superstable Interactions in Classical Statistical Mechanics. Comm. Math. Phys.18 (1970) 127–159.
- Y. Saisho and H. Tanaka, Stochastic Differential Equations for Mutually Reflecting Brownian Balls. Osaka J. Math. 23 (1986) 725–740.
- H. Tanemura, A System of Infinitely Many Mutually Reflecting Brownian Balls. Probability Theory and Related Fields104 (1996) 399–426.
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