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Mathematical problems of modeling stochastic nonlinear dynamic systems

Abstract

The purpose of this report is to introduce the engineer to the area of stochastic differential equations, and to point out the mathematical techniques and pitfalls in this area. Topics discussed include continuous-time Markov processes, the Fokker-Planck-Kolmogorov equations, the Ito and Stratonovich stochastic calculi, and the problem of modeling physical systems.

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Mortensen, R.E. Mathematical problems of modeling stochastic nonlinear dynamic systems. J Stat Phys 1, 271–296 (1969). https://doi.org/10.1007/BF01007481

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  • DOI: https://doi.org/10.1007/BF01007481

Key words

  • stochastic differential equations
  • continuous-time Markov processes
  • Fokker-Planck-Kolmogorov equations
  • Ito and Stratonovich stochastic calculi
  • modeling physical systems