Abstract Noise Processes

In addition to the NoiseProcess type, more general AbstractNoiseProcesses are defined. The NoiseGrid allows you to define a noise process from a set of pre-calculated points (the "normal" way). The NoiseApproximation allows you to define a new noise process as the solution to some stochastic differential equation. While these methods are only approximate, they are more general and allow the user to easily define their own colored noise to use in simulations.

The NoiseWrapper allows one to wrap a NoiseProcess from a previous simulation to reuse it in a new simulation in a way that follows the same stochastic trajectory (even if different points are hit, for example by solving with a smaller dt) in a distributionally-exact manner. It is demonstrated how the NoiseWrapper can be used to wrap the NoiseProcess of one SDE/RODE solution to reuse the same noise process in another simulation.

The VirtualBrownianTree allows one to trade speed for O(1) memory usage. Instead of storing Brownian motion increments, the VirtualBrownianTree samples recursively from the midpoint tmid of Brownian bridges, using a splittable PRNG. The recursion terminates when the query time agrees within some tolerance with tmid or when the maximum depth of the tree is reached.

Lastly, the NoiseFunction allows you to use any function of time as the noise process, while NoiseTransport lets you define a random process as the transport of a random variable or a random vector by a time-dependent function. Together, these functionalities allow you to define any colored noise process and use it efficiently and accurately in your simulations.

Alternative AbstractNoiseProcess Types

In addition to the mathematically-defined noise processes above, there exists more generic functionality for building noise processes from other noise processes, from arbitrary functions, from arrays, and from approximations of stochastic differential equations.

See the Noise Processes API for the constructor reference.