An Ito formula for domain-valued processes driven by stochastic flows |
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| Authors: | Kimberly Kinateder Patrick McDonald |
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| Affiliation: | (1) Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, USA. e-mail: kimberly.kinateder@wright.edu, US;(2) Department of Mathematics, New College of Florida, 5700 North Tamiami Trail, Sarasota, FL 34243, USA. e-mail: ptm@virtu.sar.usf.edu, US |
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| Abstract: | We consider a natural class of stochastic processes taking values in the space of smoothly bounded domains in ℝ n with compact closure. These processes are generated by stochastic flows on ℝ n which are obtained as the solutions of stochastic differential equations on ℝ n . We establish an Ito formula for smooth domain functionals, applied to processes in this class. Received: 2 March 2001 / Revised version: 10 January 2002 / Published online: 22 August 2002 |
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