Countable systems of degenerate stochastic differential equations with applications to super-Markov chains.

Bass, Richard F.; Perkins, Edwin A.

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We consider an infinite system of hard balls in $^{d}$ 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.