Stochastic partial differential equation
Encyclopedia
Stochastic partial differential equations (SPDEs) are similar to ordinary stochastic differential equations. They are essentially partial differential equations that have additional random terms. They can be exceedingly difficult to solve. However, they have strong connections with quantum field theory
and statistical mechanics
.
See also:
Kardar–Parisi–Zhang equation
Zakai equation
Kushner equation
Quantum field theory
Quantum field theory provides a theoretical framework for constructing quantum mechanical models of systems classically parametrized by an infinite number of dynamical degrees of freedom, that is, fields and many-body systems. It is the natural and quantitative language of particle physics and...
and statistical mechanics
Statistical mechanics
Statistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...
.
See also:
Kardar–Parisi–Zhang equation
Zakai equation
Zakai equation
In filtering theory the Zakai equation is a linear recursive filtering equation for the un-normalized density of a hidden state. In contrast, the Kushner equation gives a non-linear recursive equation for the normalized density of the hidden state...
Kushner equation
Kushner equation
In filtering theory the Kushner equation is an equation for the conditional probability density of the state of a stochastic non-linear dynamical system, given noisy measurements of the state. It therefore provides the solution of the nonlinear filtering problem in estimation theory...