Create SDE model from user-specified functions
SDE = sde(DriftRate, DiffusionRate)
SDE = sde(DriftRate, DiffusionRate, 'Name1', Value1, 'Name2', Value2, ...)
This function creates and displays general stochastic differential equation (SDE) models from user-defined drift and diffusion rate functions. Use SDE models to simulate sample paths of NVARS state variables driven by NBROWNS Brownian motion sources of risk over NPERIODS consecutive observation periods, approximating continuous-time stochastic processes.
Xt is an NVARS-by-1 state vector of process variables.
dWt is an NBROWNS-by-1 Brownian motion vector.
F is an NVARS-by-1 vector-valued drift-rate function.
G is an NVARS-by-NBROWNS matrix-valued diffusion-rate function.
|DriftRate||User-defined drift-rate function, denoted by F. DriftRate is
a function that returns an NVARS-by-1 drift-rate
vector when called with two inputs:|
|DiffusionRate||User-defined diffusion-rate function, denoted by G. DiffusionRate is
a function that returns an NVARS-by-NBROWNS diffusion-rate
matrix when called 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, NVARS-by-1 column vector, or NVARS-by-NTRIALS matrix
of initial values of the state variables. |
If StartState is a scalar, sde applies the same initial value to all state variables on all trials.
If StartState is a column vector, sde applies a unique initial value to each state variable on all trials.
If StartState is a matrix, sde 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 NBROWNS-by-NBROWNS positive
semidefinite matrix, or as a deterministic function C(t) that
accepts the current time t and returns an NBROWNS-by-NBROWNS 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 NBROWNS-by-NBROWNS identity matrix representing independent Gaussian processes.
|Simulation||A user-defined simulation function or SDE simulation method. If you do not specify a value for Simulation, the default method is simulation by Euler approximation (simByEuler).|
Stochastic differential equation model (SDE) with the following parameters:
When you specify the required input parameters as arrays, they are associated with a specific parametric form. By contrast, when you specify either required input parameter as a function, you can customize virtually any specification.
Accessing the output parameters with no inputs simply returns the original input specification. Thus, when you invoke these parameters with no inputs, they behave like simple properties and allow you to test the data type (double vs. function, or equivalently, static vs. dynamic) of the original input specification. This is useful for validating and designing methods.
When you invoke these parameters with inputs, they behave like functions, giving the impression of dynamic behavior. The parameters accept the observation time t and a state vector Xt, and return an array of appropriate dimension. Even if you originally specified an input as an array, sde treats it as a static function of time and state, thereby guaranteeing that all parameters are accessible by the same interface.
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