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An Ito formula for domain-valued processes driven by stochastic flows
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  • Published: September 2002

An Ito formula for domain-valued processes driven by stochastic flows

  • Kimberly Kinateder1 &
  • Patrick McDonald2 

Probability Theory and Related Fields volume 124, pages 73–99 (2002)Cite this article

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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.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Wright State University, Dayton, OH 45435, USA. e-mail: kimberly.kinateder@wright.edu, , , , , , US

    Kimberly Kinateder

  2. Department of Mathematics, New College of Florida, 5700 North Tamiami Trail, Sarasota, FL 34243, USA. e-mail: ptm@virtu.sar.usf.edu, , , , , , US

    Patrick McDonald

Authors
  1. Kimberly Kinateder
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  2. Patrick McDonald
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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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  • Issue Date: September 2002

  • DOI: https://doi.org/10.1007/s004400200201

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Keywords

  • Differential Equation
  • Stochastic Process
  • Stochastic Differential Equation
  • Domain Functional
  • Smooth Domain
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