BUILT-IN MATHEMATICA SYMBOL

StratonovichProcess

StratonovichProcess[{a, b}, x, t]
represents a Stratonovich process , where .

StratonovichProcess[{a, b, c}, x, t]
represents a Stratonovich process , where .

StratonovichProcess[..., ..., {x, x₀}, {t, t₀}]
represents a Stratonovich process with initial condition .

StratonovichProcess[..., ..., ..., ]
uses a Wiener process , with covariance .

StratonovichProcess[proc]
converts proc to a standard Stratonovich process whenever possible.

StratonovichProcess[sdeqns, expr, x, t, wdproc]
represents a Stratonovich process specified by a stochastic differential equation sdeqns, output expression expr, with state x and time t, driven by w following the process dproc.

Details and Options Details and Options

StratonovichProcess is also known as Stratonovich diffusion.
StratonovichProcess is a continuous-time and continuous-state random process.
If the drift a is an -dimensional vector and the diffusion b an ×-dimensional matrix, the process is -dimensional and driven by an -dimensional WienerProcess.
Common specifications for coefficients a and b include:
a scalar, b scalar

a scalar, b vector

a vector, b vector

a vector, b matrix
A stochastic differential equation is sometimes written as an integral equation .
The default initial time is taken to be zero, and default initial state is zero.
The default covariance is the identity matrix.
A standard Stratonovich process has output , consisting of a subset of differential states .
Processes proc that can be converted to standard StratonovichProcess form include OrnsteinUhlenbeckProcess, GeometricBrownianMotionProcess, ItoProcess, and StratonovichProcess.
The stochastic differential equations in sdeqns can be of the form , where is \[DifferentialD], which can be input using EscddEsc. The differentials and are taken to be Stratonovich differentials.
The output expression expr can be any expression involving and t.
The driving process dproc can be any process that can be converted to a standard Stratonovich process.
Method settings in RandomFunction specific to StratonovichProcess include:

	"EulerMaruyama"	Euler-Maruyama (order 1/2, default)
	"KloedenPlatenSchurz"	Kloeden-Platen-Schurz (order 3/2)
	"Milstein"	Milstein (order 1)
	"StochasticRungeKutta"	3-stage Rossler SRK scheme (order 1)
	"StochasticRungeKuttaScalarNoise"	3-stage Rossler SRK scheme for scalar noise (order 3/2)