public static StochasticManifoldPoint Apply(this IStochasticProcess process, StochasticManifoldPoint stochasticPoint, double time)
{
var diff = process.ExpectationDifferential(stochasticPoint.Expectation, time);
var prediction = process.Apply(stochasticPoint.Expectation, time);
return(new StochasticManifoldPoint(prediction.Expectation, stochasticPoint.Covariance.Conjugate(diff) + prediction.Covariance));
}
public OSquareMatrix ExpectationDifferential(IManifoldPoint point, double time)
{
var state = new State(point);
var basePoint = _baseProcess.Apply(state.BasePoint, time);
var baseDifferential = _baseProcess.ExpectationDifferential(state.BasePoint, time);
var mixedDifferential = MixedDifferential(state, basePoint.Expectation, baseDifferential, time);
var fiberDifferential = FiberDifferential(state, basePoint.Expectation, time);
var answer = new SquareMatrix(_stateSpace.Dimension);
answer.SetSubmatrix(0, 0, baseDifferential);
answer.SetSubmatrix(_baseProcess.StateSpace.Dimension, 0, mixedDifferential);
answer.SetSubmatrix(_baseProcess.StateSpace.Dimension, _baseProcess.StateSpace.Dimension, fiberDifferential);
return(answer);
}
public OMatrix ExpectationDifferential(IManifoldPoint point)
{
return(_process.ExpectationDifferential(point, _time));
}