dev.nm.stat.stochasticprocess.univariate.random

Class RandomProcess

java.lang.Object

dev.nm.stat.stochasticprocess.univariate.random.RandomProcess

All Implemented Interfaces:

RandomNumberGenerator, Seedable

Direct Known Subclasses:

RandomWalk

public abstract class RandomProcess
extends Object
implements RandomNumberGenerator

This interface represents a univariate random process a.k.a. stochastic process.

Given a probability space (Ω, F, P), a random process (or stochastic process) with state space X is a collection of X-valued random variables indexed by a set T ("time"). That is, a stochastic process F is a collection \(\{F_{t}: t \in T\}\) where each \(F_{t}\) is an X-valued random variable.

According to the Lévy-Khintchine representation, for a stochastic process, we have the Lévy triplet:

• the absolutely continuous part such that the increment dB is proportional to the square root of time increment dt;

See Also:

Lévy-Itō decomposition

Constructor Summary

Constructors

Constructor and Description
RandomProcess(TimeGrid timeGrid) Construct a univariate random process.

Method Summary

Modifier and Type	Method and Description
protected double	dB(double dt) Get a Brownian motion increment.
protected double	nextTime() Get the next time point in the time grid.
void	seed(long... seeds) Seed the random number/vector/scenario generator to produce repeatable experiments.
double	time() Get the current time.
protected double	Zt() Get a Gaussian innovation.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface dev.nm.stat.random.rng.univariate.RandomNumberGenerator

nextDouble

Constructor Detail

RandomProcess

public RandomProcess(TimeGrid timeGrid)

Construct a univariate random process.

Parameters:

timeGrid - the time points

Method Detail

seed

public void seed(long... seeds)

Description copied from interface: Seedable

Seed the random number/vector/scenario generator to produce repeatable experiments.

Specified by:

seed in interface Seedable

Parameters:

seeds - the seeds

time

public double time()

Get the current time.

Returns:

the current time; NaN if nextTime() is not already called

nextTime

protected double nextTime()

Get the next time point in the time grid. This advances the internal clock.

Returns:

the next time point in the time grid

Zt

protected double Zt()

Get a Gaussian innovation.

Returns:

a Gaussian innovation

dB

protected double dB(double dt)

Get a Brownian motion increment.

Parameters:

dt - the time increment

Returns:

a Brownian motion increment