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.
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Received: 2 March 2001 / Revised version: 10 January 2002 / Published online: 22 August 2002
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Kinateder, K., McDonald, P. An Ito formula for domain-valued processes driven by stochastic flows. Probab Theory Relat Fields 124, 73–99 (2002). https://doi.org/10.1007/s004400200201
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DOI: https://doi.org/10.1007/s004400200201
Keywords
- Differential Equation
- Stochastic Process
- Stochastic Differential Equation
- Domain Functional
- Smooth Domain