Local time (mathematics)

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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

[\ell(t,x)=\int_0^t \delta(x-b(s))\,ds]

where [b(s)] is the diffusion process. The basic idea is that [\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

 

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