Documentation 
Construct stochastic differential equation from linear driftrate models
SDE = sdeld(A, B, Alpha, Sigma)
SDE = sdeld(A, B, Alpha, Sigma, 'Name1', Value1, 'Name2', Value2, ...)
This constructor creates and displays SDE objects whose drift rate is expressed in linear driftrate form and that derive from the SDEDDO (SDE from drift and diffusion objects class).
Use SDELD objects to simulate sample paths of NVARS state variables expressed in linear driftrate form. They provide a parametric alternative to the meanreverting drift form (see sdemrd).
These state variables are driven by NBROWNS Brownian motion sources of risk over NPERIODS consecutive observation periods, approximating continuoustime stochastic processes with linear driftrate functions.
This method allows you to simulate any vectorvalued SDE of the form:
$$d{X}_{t}=(A(t)+B(t){X}_{t})dt+D(t,{X}_{t}^{\alpha (t)})V(t)d{W}_{t}$$  (1810) 
where:
X_{t} is an NVARSby1 state vector of process variables.
A is an NVARSby1 vector.
B is an NVARSbyNVARS matrix.
D is an NVARSbyNVARS diagonal matrix, where each element along the main diagonal is the corresponding element of the state vector raised to the corresponding power of α.
V is an NVARSbyNBROWNS instantaneous volatility rate matrix.
dW_{t} is an NBROWNSby1 Brownian motion vector.
Specify required input parameters as one of the following types:
A MATLAB^{®} array. Specifying an array indicates a static (nontimevarying) parametric specification. This array fully captures all implementation details, which are clearly associated with a parametric form.
A MATLAB function. Specifying a function provides indirect support for virtually any static, dynamic, linear, or nonlinear model. This parameter is supported via an interface, because all implementation details are hidden and fully encapsulated by the function.
Note: You can specify combinations of array and function input parameters as needed. Moreover, a parameter is identified as a deterministic function of time if the function accepts a scalar time t as its only input argument. Otherwise, a parameter is assumed to be a function of time t and state X(t) and is invoked with both input arguments. 
The required input parameters are:
A  A represents the parameter A.
If you specify A as an array, it must be an NVARSby1 column
vector of intercepts. As a deterministic function of time, when A is
called with a realvalued scalar time t as its
only input, A must produce an NVARSby1 column
vector. If you specify A as a function of time
and state, it must generate an NVARSby1 column
vector of intercepts when invoked with two inputs:

B  B represents the parameter B.
If you specify B as an array, it must be an NVARSbyNVARS matrix
of state vector coefficients. As a deterministic function of time,
when B is called with a realvalued scalar time t as
its only input, B must produce an NVARSbyNVARS matrix.
If you specify B as a function of time and state,
it must generate an NVARSbyNVARS matrix
of state vector coefficients when invoked with two inputs:

Alpha  Alpha determines the format of the parameter D.
If you specify Alpha as an array, it represents
an NVARSby1 column vector
of exponents. As a deterministic function of time, when Alpha is
called with a realvalued scalar time t as its
only input, Alpha must produce an NVARSby1 column
vector. If you specify it as a function of time and state, it must
return an NVARSby1 column
vector of exponents when invoked with two inputs:

Sigma  Sigma represents the parameter V.
If you specify Sigma as an array, it represents
is an NVARSbyNBROWNS 2dimensional
matrix of instantaneous volatility rates. In this case, each row
of Sigma corresponds to a particular state variable.
Each column of Sigma corresponds to a particular
Brownian source of uncertainty, and associates the magnitude of the
exposure of state variables with sources of uncertainty. As a deterministic
function of time, when Sigma is called with a realvalued
scalar time t as its only input, Sigma must
produce an NVARSbyNBROWNS matrix.
If you specify it as a function of time and state, it must generate
an NVARSbyNBROWNS matrix of
volatility rates when invoked with two inputs:

Specify optional inputs as matching parameter name/value pairs as follows:
Specify the parameter name as a character string, 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 string 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, NVARSby1 column vector, or NVARSbyNTRIALS matrix
of initial values of the state variables. If StartState is a scalar, sdeld applies the same initial value to all state variables on all trials. If StartState is a column vector, sdeld applies a unique initial value to each state variable on all trials. If StartState is a matrix, sdeld applies a unique initial value to each state variable on each trial. If you do not specify a value for StartState, all variables start at 1. 
Correlation  Correlation between Gaussian random variates drawn to generate
the Brownian motion vector (Wiener processes). Specify Correlation as
an NBROWNSbyNBROWNS positive
semidefinite matrix, or as a deterministic function C(t) that
accepts the current time t and returns an NBROWNSbyNBROWNS positive
semidefinite correlation matrix. A Correlation matrix represents a static condition. As a deterministic function of time, Correlation allows you to specify a dynamic correlation structure. If you do not specify a value for Correlation, the default is an NBROWNSbyNBROWNS identity matrix representing independent Gaussian processes. 
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  Object of class sdeld with the following parameters:

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