Stochastic Calculus
Stochastic calculus
is a branch of
mathematics
that operates on
stochastic processes
. The operations include integration and differentiation that involve both deterministic and
random (i.e. stochastic) variables
. It is used to model random behaviors encountered. The most well-known stochastic process to which stochastic calculus is applied is the
Wiener process
(named in honor of
Norbert Wiener
), which is used for modelling
Brownian motion
as described by
Albert Einstein
and other physical
diffusion
processes in space of particles subject to random forces. More recently, the Wiener process has been widely applied in
financial mathematics
to model the evolution in time of stock and bond prices. The main flavours of stochastic calculus are the
It calculus
and the
Malliavin calculus
.
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