Diffusion Processes and their Sample Paths

Volume 125 of the series Classics in Mathematics pp 164-211

Time changes and killing

  • Kiyosi ItôAffiliated withRIMS, Kyoto UniversityCornell University
  • , Henry P. McKeanJr.Affiliated withCourant Institute of Mathematical Sciences, New York University

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Given a 1-dimensional diffusion, singular or not, a complete description of its generator G is now before us. G coincides on its domain with a differential operator G• of degree ≦2 expressed in terms of invariants (scale, speed measure, etc.) via the formulas 4.1.8) [or 4.1.31,32,33)] and each invariant has a simple probabilistic meaning embodied in the formulas 4.1.7) [or 4.1.22, 23 b, 23 c, and 26)].