page_title: Local time (mathematics)
hierarchical_section_title: Local time (mathematics)
caption_attribution_description: A sample path of an Itō process together with its surface of local times. The example used is an Ornstein-Uhlenbeck process satisfying the stochastic differential equation dX&#160;=&#160;dB&#160;-&#160;5X&#160;dt.
context_page_description: In the mathematical theory of stochastic processes, local time is a stochastic process associated with semimartingale processes such as Brownian motion, that characterizes the amount of time a particle has spent at a given level. Local time appears in various stochastic integration formulas, such as Tanaka's formula, if the integrand is not sufficiently smooth. It is also studied in statistical mechanics in the context of random fields.
context_section_description: In the mathematical theory of stochastic processes, local time is a stochastic process associated with semimartingale processes such as Brownian motion, that characterizes the amount of time a particle has spent at a given level. Local time appears in various stochastic integration formulas, such as Tanaka's formula, if the integrand is not sufficiently smooth. It is also studied in statistical mechanics in the context of random fields.
caption: A sample path of an Itō process together with its surface of local times.
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