Reflecting Ornstein-Uhlenbeck processes on pinned path spaces

Details Reflecting Ornstein-Uhlenbeck processes on pinned path spaces Reflecting Ornstein-Uhlenbeck processes on pinned path spaces

2007-11-14

arxiv.org/abs/0711.2144v1

Proceedings of RIMS Workshop on Stochastic Analysis and Applications, 111-128, RIMS Kokyuroku Bessatsu, B6, Res. Inst. Math. S

Mathematics

Probability

19 pages

Scientific paper

Consider a set of continuous maps from the interval $[0,1]$ to a domain in ${\mathbb R}^d$. Although the topological boundary of this set in the path space is not smooth in general, by using the theory of functions of bounded variation (BV functions) on the Wiener space and the theory of Dirichlet forms, we can discuss the existence of the surface measure and the Skorokhod representation of the reflecting Ornstein-Uhlenbeck process associated with the canonical Dirichlet form on this set.

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