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In the mathematical theory of stochastic processes, local time is a property of diffusions like Brownian motion. Formally, it is given by

<math>\ell(t,x)=\int_0^t \delta(x-b(s))\,ds</math>

where <math>b(s)</math> is the diffusion process. The basic idea is that <math>\ell(t,x)</math> is a (rescaled) measure of how much time <math>b(s)</math> has spent at <math>x</math> up to time <math>t</math>.

[edit] See also

• Diffusion
• Brownian motion
• Red noise, also known as brown noise (Martin Gardner proposed this name for sound generated with random intervals. It is a pun on Brownian motion and white noise.)
• Diffusion equation