Construct SDE model from userspecified functions
SDE = sde(DriftRate, DiffusionRate)
SDE = sde(DriftRate, DiffusionRate, 'Name1', Value1,
'Name2', Value2, ...)
This constructor creates and displays general stochastic differential
equation (SDE
) models from userdefined drift and
diffusion rate functions. Use sde
objects to simulate
sample paths of NVARS
state variables driven by NBROWNS
Brownian
motion sources of risk over NPERIODS
consecutive
observation periods, approximating continuoustime stochastic processes.
This constructor enables you to simulate any vectorvalued SDE of the form:
$$d{X}_{t}=F(t,{X}_{t})dt+G(t,{X}_{t})d{W}_{t}$$  (185) 
where:
X_{t} is an NVARS
by1
state
vector of process variables.
dW_{t} is an NBROWNS
by1
Brownian
motion vector.
F is an NVARS
by1
vectorvalued
driftrate function.
G is an NVARS
byNBROWNS
matrixvalued
diffusionrate function.
DriftRate  Userdefined driftrate function, denoted by F. DriftRate is
a function that returns an NVARS by1 driftrate
vector when called with two inputs:
DriftRate may also
be an object of class Drift that encapsulates the
driftrate specification. In this case, however, sde uses
only the Rate parameter of the object. 
DiffusionRate  Userdefined diffusionrate function, denoted by G. DiffusionRate is
a function that returns an NVARS byNBROWNS diffusionrate
matrix when called with two inputs:
DiffusionRate may
also be an object of class Diffusion that encapsulates
the diffusionrate specification. In this case, however, sde uses
only the Rate parameter of the object. 
Specify optional inputs as matching parameter name/value pairs as follows:
Specify the parameter name as a character vector, followed by its corresponding value.
You can specify parameter name/value pairs in any order.
Parameter names are case insensitive.
You can specify unambiguous partial character vector matches.
Valid parameter names are:
StartTime  Scalar starting time of the first observation, applied to all
state variables. If you do not specify a value for StartTime ,
the default is 0 . 
StartState  Scalar, NVARS by1 column
vector, or NVARS byNTRIALS matrix
of initial values of the state variables. If If If If you do not specify
a value for 
Correlation  Correlation between Gaussian random variates drawn to generate
the Brownian motion vector (Wiener processes). Specify Correlation as
an NBROWNS byNBROWNS positive
semidefinite matrix, or as a deterministic function C(t) that
accepts the current time t and returns an NBROWNS byNBROWNS positive
semidefinite correlation matrix. A As a deterministic function
of time, If you do not specify a value for 
Simulation  A userdefined simulation function or SDE simulation method.
If you do not specify a value for Simulation , the
default method is simulation by Euler approximation (simByEuler ). 
SDE  Stochastic differential equation model (

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