shape + ( n ,), scale = delta * sqrt ( dt )) # If `out` was not given, create an output array. asarray ( x0 ) # For each element of x0, generate a sample of n numbers from a # normal distribution. Note that the initial value `x0` is not included in the returned array.
Returns - A numpy array of floats with shape `x0.shape + (n,)`. If `out` is None, a new numpy array is created and returned. out : numpy array or None If `out` is not None, it specifies the array in which to put the result. The random variable of the position at time t, X(t), has a normal distribution whose mean is the position at time t=0 and whose variance is delta**2*t. delta : float delta determines the "speed" of the Brownian motion. Arguments - x0 : float or numpy array (or something that can be converted to a numpy array using numpy.asarray(x0)). Written as an iteration scheme, X(t + dt) = X(t) + N(0, delta**2 * dt t, t+dt) If `x0` is an array (or array-like), each value in `x0` is treated as an initial condition, and the value returned is a numpy array with one more dimension than `x0`. The parameters t0 and t1 make explicit the statistical independence of N on different time intervals that is, if [t0, t1) and [t2, t3) are disjoint intervals, then N(a, b t0, t1) and N(a, b t2, t3) are independent. the Wiener process): X(t) = X(0) + N(0, delta**2 * t 0, t) where N(a,b t0, t1) is a normally distributed random variable with mean a and variance b. """ # File: brownian.py from math import sqrt from scipy.stats import norm import numpy as np def brownian ( x0, n, dt, delta, out = None ): """ Generate an instance of Brownian motion (i.e. """ brownian() implements one dimensional Brownian motion (i.e.
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