Phase Space Transformations of Gaussian Diffusions |
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| Authors: | Brand? Augusto Kolsrud Torbj?rn |
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| Affiliation: | (1) Portuga, Grupo de Física Matemática, University of Lisbon, Universidade de Lisboa, Av. Prof. Gama Pinto 2, 1699 Lisboa Codex, Portugal E-mail;(2) Royal Institute of Technology, Stockholm, Sweden;(3) Kungliga Tekniska Högskolan, Matematiska Institutionen, S-100 44 Stockholm, Sweden E-mail |
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| Abstract: | It is shown that for Gaussian diffusions, the transformation back to Brownian motion, usually accomplished via the Girsanov (or Feynman–Kac) formula and time-shift, can be obtained by a classical canonical, i.e. symplectic, transformation in phase space. The method is based on constants of motion, in this case the Wronskian. Similar transformations for general diffusions are briefly discussed. |
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| Keywords: | Diffusion processes Gaussian diffusion Feynman– Kac formula Girsanov formula heat equation potential constant of motion symplectic transformation Liouville integrability Wronskian. |
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