represents the most general model.
SDE object requires the following
A drift-rate function
This function returns an
vector when run with the following inputs:
A real-valued scalar observation time t.
A diffusion-rate function
function returns an
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.
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 the
to create an object
obj of class
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
obj 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
NVARS-by-1 column vector)
Correlation: The correlation structure
between Brownian process
Drift: The drift-rate function F(t,Xt)
Diffusion: The diffusion-rate
Simulation: The simulation method
Of these displayed parameters, only
The only exception to the (t, Xt)
evaluation interface is
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.