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

$\backslash ell(t,x)=\backslash int\_0^t\; \backslash delta(x-b(s))\backslash ,ds$

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

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

Stochastic processes | Fractals | Statistical mechanics