Ornstein-Uhlenbeck process
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Ornstein-Uhlenbeck process
Figure 2: Two realizations of the Ornstein-Uhlenbeck process for parameters τ=1.0 and σ=0.1 (black curve), and for τ=0.1 and σ=0.31622 (red curve). In both cases the noise intensity is σ^2*τ=0.01 . The red curve represents a noise that more closely mimics Gaussian white noise. Both realizations begin here at x(0)=1.0 , after which the mean decays exponentially to zero with time constant τ.
Andre Longtin (2010) Stochastic dynamical systems. Scholarpedia, 5(4):1619.
Sebastian Schmitt, 2022
.. code-block:: python
// ornstein_uhlenbeck.py
from brian2 import *
N = NeuronGroup(
1,
"""
tau : second
sigma : 1
dy/dt = -y/tau + sqrt(2*sigma**2/tau)*xi : 1
""",
method="euler"
)
N.tau = 0.5 * second
N.sigma = 0.1
N.y = 1
M = StateMonitor(N, "y", record=True)
run(10 * second)
.. code-block:: html
Brian2 WASM Simulation