OUProcess

class brainpy.dyn.OUProcess(size, mean=0.0, sigma=1.0, tau=10.0, method='exp_euler', keep_size=False, mode=None, name=None)

The Ornstein–Uhlenbeck process.

The Ornstein–Uhlenbeck process \(x_{t}\) is defined by the following stochastic differential equation:

\[\tau dx_{t}=-\theta \,x_{t}\,dt+\sigma \,dW_{t}\]

where \(\theta >0\) and \(\sigma >0\) are parameters and \(W_{t}\) denotes the Wiener process.

Parameters:

• size (int, sequence of int) – The model size.

• mean (Parameter) – The noise mean value.

• sigma (Parameter) – The noise amplitude.

• tau (Parameter) – The decay time constant.

• method (str) – The numerical integration method for stochastic differential equation.

• name (str) – The model name.

update()

The function to specify the updating rule.