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Rong-feng Sun

2009-10-16
10:30:00 - 12:00:00

Stochastic flows of kernels in the Brownian net and the Brownian web

405 , Mathematics Research Center Building (ori. New Math. Bldg.)

Le Jan and Raimond developed a theory of stochastic flows of kernels, showing that each consistent family of n-point motions gives rise to a stochastic flow of kernel. As an example, they constructed a special family of such flows where the underlying one-point motion is a Brownian motion on R. Recently, Howitt and Warren introduced a much more general class such flows on R, where the underlying n-point motions are Brownian motions with sticky interactions upon collision. Stochastic flows of kernels can be interpretated as random motion in a stationary space-time random environment, where the environment satisfies certain independent innovation properties. Here we give a graphical construction of the underlying environment for the Howitt-Warren flow in terms of the Brownian net (resp. the Brownian web), which loosely speaking consists of a collection of branching-coalescing (resp. coalescing) Brownian motions starting from every point in the space-time plane. Almost sure path properties for the Howitt-Warren flow will also be derived. This is based on joint work in progress with Jan M. Swart (UTIA, Prague) and Emmanuel Schertzer (Columbia, New York).