Please tell us which country and city you'd like to see the weather in.
Time zone
A time zone is a region that observes a uniform standard time for legal, commercial, and social purposes. Time zones tend to follow the boundaries of countries and their subdivisions because it is convenient for areas in close commercial or other communication to keep the same time.
Most of the time zones on land are offset from Coordinated Universal Time (UTC) by a whole number of hours (UTC−12 to UTC+14), but a few are offset by 30 or 45 minutes (for example Newfoundland Standard Time is UTC−03:30, Nepal Standard Time is UTC+05:45, and Indian Standard Time is UTC+05:30). Some higher latitude countries use daylight saving time for part of the year, typically by changing clocks by an hour. Many land time zones are skewed toward the west of the corresponding nautical time zones. This also creates a permanent daylight saving time effect.
History
Early timekeeping
Before clocks were first invented, it was common practice to mark the time of day with apparent solar time (also called "true" solar time) – for example, the time on a sundial – which was typically different for every settlement.
Local time (mathematics)
In the mathematical theory of stochastic processes, local time is a stochastic process associated with diffusion 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.
Formal definition
For a real valued diffusion process 
, the local time of 
at the point 
is the stochastic process
where 
is the Dirac delta function. It is a notion invented by Paul Lévy. The basic idea is that 
is a (rescaled) measure of how much time 
has spent at up to time 
. It may be written as
which explains why it is called the local time of 
at . For a discrete state-space process 
, the local time can be expressed more simply as
Tanaka's Formula
Tanaka's formula provides a definition of local time for an arbitrary continuous semimartingale on 
