represents the most general model.
sde object using the
requires the following inputs:
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.
sde constructor 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;
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
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.