• Corpus ID: 119591665

The intrinsic "sense" of stochastic differential equations

  title={The intrinsic "sense" of stochastic differential equations},
  author={Dietrich Ryter},
  journal={arXiv: Mathematical Physics},
  • D. Ryter
  • Published 10 May 2016
  • Mathematics
  • arXiv: Mathematical Physics
A free choice of the integration sense would lead to the paradox that the number of possible equations (thus of solutions for a given model) can vary under a mere change of the variables. This is shown by a specific change which neutralizes the sense (by establishing a constant coupling with the noise). Its inverse singles out the Stratonovich sense, by means of the Ito formula. 

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Fokker-Planck equations are decisive for the Markov property. With multiplicative noise they have non-Gaussian solutions in short times. Corresponding new path increments agree with a FPE by both

Revised numerical solutions of stochastic differential equations with multiplicative noise, and the evolution of density peaks

The Fokker-Planck equation involves a drift (given by derivatives of the diffusion), which is absent in the SDE. Increments of the random paths must include that drift. This corrects the existing



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The solutions of SDEs with multiplicative noise are not Markovian. On a coarse-grained time scale they still are, but only in the "anti-Ito" case. This allows a simple computation of the most likely

Stochastische Differentialgleichungen (Oldenbourg

  • München, 1973) , and Stochastic Differential Equations: Theory and Applications
  • 1974

Skorochod, Stochastische Differentialgleichungen (Akademie- Verlag, Berlin

  • 1971