Stochastic Processes

Detailed Description

Functions
template<typename Generator , uint32 DIM>
Vector< float, DIM >	cugar::brownian_bridge (const uint32 L, const uint32 t, Generator gaussian)
template<uint32 DIM, typename Distribution , typename Sampler_type >
Vector< float, DIM >	cugar::generate_point (Sampler_type &sampler, Distribution &gaussian)
template<uint32 DIM, typename Sequence , typename Distribution >
Vector< float, DIM >	cugar::brownian_bridge (Distribution &gaussian, const float sigma, const uint32 N, const uint32 i, const uint32 L, const uint32 t, const Sequence &sequence)

Function Documentation

brownian_bridge() [1/2]

template<typename Generator , uint32 DIM>

Vector< float, DIM > cugar::brownian_bridge	(	const uint32	L,
		const uint32	t,
		Generator	gaussian
	)

Evaluate a DIM-dimensional Brownian bridge of length L at time t, using a black-box Gaussian generator.

brownian_bridge() [2/2]

template<uint32 DIM, typename Sequence , typename Distribution >

Vector< float, DIM > cugar::brownian_bridge	(	Distribution &	gaussian,
		const float	sigma,
		const uint32	N,
		const uint32	i,
		const uint32	L,
		const uint32	t,
		const Sequence &	sequence
	)

Evaluate the i/N-th DIM-dimensional Brownian bridge of length L at time t. The bridges are created using L copies of a DIM-dimensional Sobol sequence, first permuted and then shifted through Cranley-Patterson rotations. The vector of permutations must contain L permutations of the indices [0,N-1], and the vector of rotations must contain L * (DIM + (DIM & 1)) entries.

generate_point()

template<uint32 DIM, typename Distribution , typename Sampler_type >

Vector< float, DIM > cugar::generate_point	(	Sampler_type &	sampler,
		Distribution &	gaussian
	)

A simple utility function to generate a DIM-dimensional Gaussian point using the i-th point of a sample sequence, shifted by a Cranley-Patterson rotation.