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sequence convergence - python

Good “frequent sequence mining” packages in Python?Is the percepetron algorithm's convergence dependent on the linearity of the data?Convergence of vanilla or natural policy gradients (e.g. REINFORCE)Very slow convergence with CNNTuning a sequence to sequence modelSequence to sequence RNN model, maximum number of training sizeGenerating a sequence based on value in another column in PythonSequence extraction in a datasetUsing VAE with Sequence to Sequence ApproachSequence classification using oneClass SVM

0

$begingroup$

. Let pi : i ∈ Z be an iid sequence with pi ∈ (0, 1).
Fix this random environment, then consider the random walk
P[ Xn+1 = i + 1 | Xn = i] = 1 − P[ Xn+1 = i − 1 | Xn = i] = pi.

(a) Let pi be 1/3 or 2/3, with probability 1/2 each. Find a deterministic sequence an such that Xn/an
seems to be converging in distribution to a non-degenerate variable.

(b) Find a distribution with Epi = 1/2 such that Xn is transient.

(c) In both cases, draw pictures of the space-time trajectorie

I need to simulate the above,I have started working on (a) but I don't get how to find such a sequence.
here is my code for the random walk:

import random
import numpy as np 
import matplotlib.pyplot as plt 

prob = [0.333333333333333333,0.666666666666666666]

start = 0 
positions = [start] 

rr = np.random.random(1000) 
downp = rr < prob[0] 
upp = rr > prob[1]

for idownp, iupp in zip(downp, upp):
 down = idownp and positions[-1] > -100
 up = iupp and positions[-1] < 100
 positions.append(positions[-1] - down + up)

plt.plot(positions) 
plt.show() 

how can I proceed??

python convergence

share|improve this question

asked 23 mins ago

Med QadiMed Qadi

1

New contributor

Med Qadi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

0

$begingroup$

. Let pi : i ∈ Z be an iid sequence with pi ∈ (0, 1).
Fix this random environment, then consider the random walk
P[ Xn+1 = i + 1 | Xn = i] = 1 − P[ Xn+1 = i − 1 | Xn = i] = pi.

(a) Let pi be 1/3 or 2/3, with probability 1/2 each. Find a deterministic sequence an such that Xn/an
seems to be converging in distribution to a non-degenerate variable.

(b) Find a distribution with Epi = 1/2 such that Xn is transient.

(c) In both cases, draw pictures of the space-time trajectorie

I need to simulate the above,I have started working on (a) but I don't get how to find such a sequence.
here is my code for the random walk:

import random
import numpy as np 
import matplotlib.pyplot as plt 

prob = [0.333333333333333333,0.666666666666666666]

start = 0 
positions = [start] 

rr = np.random.random(1000) 
downp = rr < prob[0] 
upp = rr > prob[1]

for idownp, iupp in zip(downp, upp):
 down = idownp and positions[-1] > -100
 up = iupp and positions[-1] < 100
 positions.append(positions[-1] - down + up)

plt.plot(positions) 
plt.show() 

how can I proceed??

python convergence

share|improve this question

asked 23 mins ago

Med QadiMed Qadi

1

New contributor

Med Qadi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

add a comment | 

$begingroup$

. Let pi : i ∈ Z be an iid sequence with pi ∈ (0, 1).
Fix this random environment, then consider the random walk
P[ Xn+1 = i + 1 | Xn = i] = 1 − P[ Xn+1 = i − 1 | Xn = i] = pi.

(a) Let pi be 1/3 or 2/3, with probability 1/2 each. Find a deterministic sequence an such that Xn/an
seems to be converging in distribution to a non-degenerate variable.

(b) Find a distribution with Epi = 1/2 such that Xn is transient.

(c) In both cases, draw pictures of the space-time trajectorie

I need to simulate the above,I have started working on (a) but I don't get how to find such a sequence.
here is my code for the random walk:

import random
import numpy as np 
import matplotlib.pyplot as plt 

prob = [0.333333333333333333,0.666666666666666666]

start = 0 
positions = [start] 

rr = np.random.random(1000) 
downp = rr < prob[0] 
upp = rr > prob[1]

for idownp, iupp in zip(downp, upp):
 down = idownp and positions[-1] > -100
 up = iupp and positions[-1] < 100
 positions.append(positions[-1] - down + up)

plt.plot(positions) 
plt.show() 

how can I proceed??

python convergence

share|improve this question

asked 23 mins ago

Med QadiMed Qadi

1

New contributor

Med Qadi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

import random
import numpy as np 
import matplotlib.pyplot as plt 

prob = [0.333333333333333333,0.666666666666666666]

start = 0 
positions = [start] 

rr = np.random.random(1000) 
downp = rr < prob[0] 
upp = rr > prob[1]

for idownp, iupp in zip(downp, upp):
 down = idownp and positions[-1] > -100
 up = iupp and positions[-1] < 100
 positions.append(positions[-1] - down + up)

plt.plot(positions) 
plt.show() 

share|improve this question

asked 23 mins ago

Med QadiMed Qadi

1

New contributor

Med Qadi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|improve this question

asked 23 mins ago

Med QadiMed Qadi

1

New contributor

Med Qadi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 23 mins ago

Med QadiMed Qadi

1

New contributor

Med Qadi is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 23 mins ago

Med QadiMed Qadi

1