Abstract
This work is concerned with the existence and uniqueness of a strong Markov process that has continuous sample paths and the following additional properties. 1. The state space is a cone ind-dimensions (d≧3), and the process behaves in the interior of the cone like ordinary Brownian motion. 2. The process reflects instantaneously at the boundary of the cone, the direction of reflection is continuous except at the vertex and has a limit which is fixed on each radial line emanating from the vertex. 3. The amount of time that the process spends at the vertex of the cone is zero (i.e., the set of times for which the process is at the vertex has zero Lebesgue measure.)
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