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Continuous stochastic processes are introduced through the Chapman-Kolmogorov equation and then the Fokker-Planck equation. The role of barriers and thus the concept of exit time are discussed. Finally, stochastic differential equations and Ito’s formula are introduced, illustrated with some examples, and the mechanism of stochastic resonance is discussed in detail.

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Stochastic Processes with Continuous States and Time

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  • 发表日期：

    2026年

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  • Guido Boffetta,
  • Angelo Vulpiani

摘要

Continuous stochastic processes are introduced through the Chapman-Kolmogorov equation and then the Fokker-Planck equation. The role of barriers and thus the concept of exit time are discussed. Finally, stochastic differential equations and Ito’s formula are introduced, illustrated with some examples, and the mechanism of stochastic resonance is discussed in detail.