Base SDE Models
represents the most general model.
sde object using
sde requires the following inputs:
A drift-rate function
F. This function returns an
1drift-rate vector when run with the following inputs:
A real-valued scalar observation time t.
1state vector Xt.
A diffusion-rate function
G. This function returns an
NBrownsdiffusion-rate matrix when run with the inputs t and Xt.
Evaluating object parameters by passing (t, Xt) to a common, published interface allows most parameters to be referenced by a common input argument list that reinforces common method programming. You can use this simple function evaluation approach to model or construct powerful analytics, as in the following example.
Example: Base SDE Models
sde object using
sde to represent a univariate
geometric Brownian Motion model of the form:
Create drift and diffusion functions that are accessible by the common (t,Xt) interface:
F = @(t,X) 0.1 * X; G = @(t,X) 0.3 * X;
Pass the functions to
sdeto create an
obj = sde(F, G) % dX = F(t,X)dt + G(t,X)dW
obj = Class SDE: Stochastic Differential Equation ------------------------------------------- Dimensions: State = 1, Brownian = 1 ------------------------------------------- StartTime: 0 StartState: 1 Correlation: 1 Drift: drift rate function F(t,X(t)) Diffusion: diffusion rate function G(t,X(t)) Simulation: simulation method/function simByEuler
sde object displays like a MATLAB® structure, with the following information:
The object's class
A brief description of the object
A summary of the dimensionality of the model
The object's displayed parameters are as follows:
StartTime: The initial observation time (real-valued scalar)
StartState: The initial state vector (
Correlation: The correlation structure between Brownian process
Drift: The drift-rate function F(t,Xt)
Diffusion: The diffusion-rate function G(t,Xt)
Simulation: The simulation method or function.
Of these displayed parameters, only
Diffusion are required inputs.
The only exception to the (t,
Xt) evaluation interface is
Correlation. Specifically, when you enter
Correlation as a function, the SDE engine assumes that it is
a deterministic function of time, C(t). This restriction on
Correlation as a
deterministic function of time allows Cholesky factors to be computed and stored
before the formal simulation. This inconsistency dramatically improves run-time
performance for dynamic correlation structures. If
stochastic, you can also include it within the simulation architecture as part of a
more general random number generation function.