GeneralizedDirichlet.hpp file
Lochner's generalized Dirichlet SDE.
Contents
- Reference
This file implements the time integration of a system of stochastic differential equations (SDEs) whose invariant is Lochner's generalized Dirichlet distribution.
In a nutshell, the equation integrated governs a set of scalars, , , , as
where is an isotropic vector-valued Wiener process with independent increments. The statistically stationary solution of the above coupled system of nonlinear stochastic differential equations is the generalized Dirichlet distribution,
provided the coefficients, , , , and , with for , , satisfy
Here
,
, and
are parameters, while
for
, and
.
denotes the gamma function. To keep the invariant distribution generalized Dirichlet, the above set of constraints on the coefficients must be satisfied. For more details on the generalized Dirichlet SDE, see https:/
Namespaces
- namespace walker
- Walker declarations and definitions.
Classes
-
template<class Init, class Coefficients>class walker::GeneralizedDirichlet
- Lochner's generalized Dirichlet SDE used polymorphically with DiffEq.