A Modeller's Introduction to Stochastic Nonlinear Dynamics:
Stochastic differential equations, Fokker-Planck equations, and noise-induced escape

An introduction to stochastic differential equations, Fokker-Planck equations, and mean first passage times, working towards noise-induced escape in a one-dimensional bistable system. It is written for modellers coming from deterministic nonlinear dynamics rather than for mathematicians or physicists: instead of beginning with Markov processes or Langevin dynamics, it starts from a deterministic differential equation, adds noise to it naively, and only then works out what the resulting equation means. Only additive white Gaussian noise is considered.

This is a lightly edited standalone version of Chapter 2 of my doctoral thesis (the University of Tokyo, 2026), which is not publicly available yet.

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Please cite as: H. Ishii, "A modeller's introduction to stochastic nonlinear dynamics" (2026), adapted from Chapter 2 of the author's doctoral thesis.

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