utils.solver.euler_maruyama_method

utils.solver.euler_maruyama_method(
    f,
    t_span,
    y0,
    dt,
    noise_func=None,
    rng=None,
    args=(),
    post_step=None,
)

Fixed-step Euler-Maruyama integrator for stochastic differential equations.

Solves:

dy = f(t, y) dt + noise_func(t, y) dW

where dW is a Wiener increment with variance dt.

Parameters

f : callable: Drift function with signature f(t, y, *args).
t_span : tuple of float: (t0, tf) integration bounds.
y0 : array - like: Initial state vector.
dt : float: Fixed timestep.
noise_func : callable or None = None: Diffusion function with signature noise_func(t, y), returning a vector of per-state diffusion scales. If None, the stochastic term is zero and deterministic Euler is recovered.
rng : numpy.random.Generator or None = None: Random generator for Wiener increments. A fresh generator is created if None.
args : tuple = (): Extra positional arguments forwarded to f.
post_step : callable or None = None: Optional hook called after each accepted step with signature post_step(t, y) -> y. The returned array replaces the current state, allowing post-step corrections (e.g. state nudging).

solution : Solution: Object with attributes t (time axis) and y (state trajectory).

: ValueError: If noise_func returns a vector whose shape does not match the state vector.