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# VectorBrownianMotion Class Reference

`#include <StochasticProcesses.h>`

Inheritance diagram for VectorBrownianMotion: List of all members.

## Detailed Description

Brownian motion in any dimension.

Definition at line 77 of file StochasticProcesses.h.

## Public Member Functions

VectorBrownianMotion (int dim, int T, Real dt)
VectorBrownianMotion (int dim, int T, Real dt, RealVector &x0)
void timeStep (int t)

## Static Public Member Functions

void testPathFunctional (int t, int T, int nPath)

## Constructor & Destructor Documentation

 VectorBrownianMotion::VectorBrownianMotion ( int dim, int T, Real dt )

Brownian motion starts at zero.

Parameters:
 dim dimension. T number of time steps to horizon. dt size of time step.

 VectorBrownianMotion::VectorBrownianMotion ( int dim, int T, Real dt, RealVector & x0 )

Parameters:
 dim dimension. T number of time steps to horizon. dt size of time step. x starting point of Brownian motion.

## Member Function Documentation

 void VectorBrownianMotion::timeStep ( int t ) ` [virtual]`
 Time step t->t+1 based on current Z-increments. Implements StochasticProcess< RealVector, Real >.

 void VectorBrownianMotion::testPathFunctional ( int t, int T, int nPath ) ` [static]`
 Allocates a two dimensional Brownian motion X with T time steps of size dt=0.01 to the horizon. The path functional f is defined to be f=X_1(T)+X_2(T). A path of X is computed to time t and the functional conditioned on the state at time t. The conditional distribution is normal with mean X_1(t)+X_2(t) and variance 2*(T-t)*dt. The conditional mean and variance are computed from a sample of size nPath and compared with the analytic values.

The documentation for this class was generated from the following file:
Generated on Mon Sep 22 02:16:33 2003 for Libor-Library by 1.3-rc3