# 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. Zbl0192.61801
- M. Fradon and S. Rœlly, Infinite dimensional diffusion processes with singular interaction. Bull. Sci. math. 124 (2000) 287–318. Zbl0958.60059
- J. Fritz, Gradient Dynamics of Infinite Points Systems. Ann Probab.15 (1987) 478–514. Zbl0623.60119
- 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. Zbl0349.60103
- D. Ruelle, Superstable Interactions in Classical Statistical Mechanics. Comm. Math. Phys.18 (1970) 127–159. Zbl0198.31101
- Y. Saisho and H. Tanaka, Stochastic Differential Equations for Mutually Reflecting Brownian Balls. Osaka J. Math. 23 (1986) 725–740. Zbl0613.60057
- H. Tanemura, A System of Infinitely Many Mutually Reflecting Brownian Balls. Probability Theory and Related Fields104 (1996) 399–426. Zbl0849.60087

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