Mathematical and Theoretical Neuroscience by Giovanni Naldi & Thierry Nieus

Author:Giovanni Naldi & Thierry Nieus
Language: eng
Format: epub
ISBN: 9783319682976
Publisher: Springer International Publishing

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where N(0, σ 2) is a normally distributed variable with zero mean and variance equal to σ 2. This process, first described in [18], is discussed in [1, 2, 24, 30]. In particular, in [1, 2] August and Zucker introduced the Markov process that results from the Brownian motion with randomly curved paths. We denote v the probability density to find a particle at the point (x 1, x 2) considering that it started from a given location and that it is moving with some known velocity. This probability density satisfies a deterministic equation known in literature as the Kolmogorov forward equation or Fokker Planck equation:

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