Formal Definition
Mathematically, the definition of the local time is
where b(s) is the diffusion process and δ is the Dirac delta function. It is a notion invented by Paul Lévy. The basic idea is that ℓ(t, x) is a (rescaled) measure of how much time b(s) has spent at x up to time t. It may be written as
which explains why it is called the local time of b at x.
Read more about this topic: Local Time (mathematics)
Famous quotes containing the words formal and/or definition:
“The conviction that the best way to prepare children for a harsh, rapidly changing world is to introduce formal instruction at an early age is wrong. There is simply no evidence to support it, and considerable evidence against it. Starting children early academically has not worked in the past and is not working now.”
—David Elkind (20th century)
“Was man made stupid to see his own stupidity?
Is God by definition indifferent, beyond us all?
Is the eternal truth man’s fighting soul
Wherein the Beast ravens in its own avidity?”
—Richard Eberhart (b. 1904)