In [1]: import random
In [2]: import numpy as np
In [3]: import matplotlib.pyplot as plt

In [4]: position = 0
In [5]: walk = [position]
In [6]: steps = 1000
In [7]: for i in range(steps):
   ...:     step = 1 if random.randint(0, 1) else -1
   ...:     position += step
   ...:     walk.append(position)
   ...:

In [8]: plt.plot(walk[:100])
Out[8]: [<matplotlib.lines.Line2D at 0x13da0a58898>]

In [9]: plt.show()

In [34]: nsteps = 1000
In [35]: draws = np.random.randint(0, 2, size=nsteps)
In [36]: steps = np.where(draws > 0, 1, -1)
In [38]: walk = steps.cumsum()

In [39]: walk.min()
Out[39]: -34
In [40]: walk.max()
Out[40]: 14

In [41]: plt.plot(walk[:100])
Out[41]: [<matplotlib.lines.Line2D at 0x13da2c1aa90>]

In [42]: plt.show()

一次性模拟多次随机漫步

In [47]: nwalks = 5000

In [48]: nsteps = 1000

In [49]: draws = np.random.randint(0, 2, size=(nwalks, nsteps)) # 0或1

In [50]: steps = np.where(draws > 0, 1, -1)

In [51]: walks = steps.cumsum(1)

In [52]: walks
Out[52]:
array([[  1,   0,   1, ...,  18,  17,  18],
       [ -1,   0,   1, ..., -54, -55, -56],
       [  1,   2,   3, ...,  10,   9,  10],
       ...,
       [  1,   2,   3, ..., -16, -17, -16],
       [ -1,   0,   1, ...,  14,  13,  14],
       [  1,   2,   3, ...,  -8,  -9,  -8]], dtype=int32)

In [53]: walks.max()
Out[53]: 118

In [54]: walks.min()
Out[54]: -119

In [55]:

In [55]:

In [55]: hist30 = (np.abs(walks) >= 30).any(1)

In [56]: hist30
Out[56]: array([ True,  True, False, ...,  True, False, False])

In [57]: hist30.sum()
Out[57]: 3367

In [58]: np.abs(walks[hist30])
Out[58]:
array([[ 1,  0,  1, ..., 18, 17, 18],
       [ 1,  0,  1, ..., 54, 55, 56],
       [ 1,  2,  3, ..., 30, 31, 30],
       ...,
       [ 1,  0,  1, ...,  6,  5,  4],
       [ 1,  2,  3, ...,  2,  3,  4],
       [ 1,  2,  3, ..., 16, 17, 16]], dtype=int32)

In [59]: np.abs(walks[hist30]) >= 30
Out[59]:
array([[False, False, False, ..., False, False, False],
       [False, False, False, ...,  True,  True,  True],
       [False, False, False, ...,  True,  True,  True],
       ...,
       [False, False, False, ..., False, False, False],
       [False, False, False, ..., False, False, False],
       [False, False, False, ..., False, False, False]])

In [60]: (np.abs(walks[hist30]) >= 30).argmax(1)
Out[60]: array([433, 337, 815, ..., 555, 603, 351], dtype=int64)

In [61]: crossing_times = (np.abs(walks[hist30]) >= 30).argmax(1)

In [62]: crossing_times.mean()
Out[62]: 504.25274725274727