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)[source]#
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 (
TypeVar(Shape,int,Tuple[int,...])) – The model size.mean (
Union[float,TypeVar(ArrayType,Array,Variable,TrainVar,Array,ndarray),Callable]) – The noise mean value.sigma (
Union[float,TypeVar(ArrayType,Array,Variable,TrainVar,Array,ndarray),Callable]) – The noise amplitude.tau (
Union[float,TypeVar(ArrayType,Array,Variable,TrainVar,Array,ndarray),Callable]) – The decay time constant.method (
str) – The numerical integration method for stochastic differential equation.name (
str) – The model name.