Intersection Local Times for Infinite Systems of Planar Brownian Motions and for the Brownian Density Process By
نویسندگان
چکیده
Let Xt,', ,..., be a sequence of independent, planar Brownian motions starting at the points of a planar Poisson process of intensity A. Let a', 02,.. .. be independent, ±1 random variables. Let Lt(X', Xi) be the intersection local time of x' and Xi up to time t. We study the limit in distribution of A-1 EZ oi'ioLt(XV,XJ) as A -* o. The resulting process is called the intersection local time for the Brownian density process, and its existence was established in a companion paper by Adler and Lewin (1988). The current paper concentrates on establishing the above limit theorem, and, as a bonus, obtains a Tanaka-like formula giving an evolution equation representation of -the Brownian density's intersection local time.
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