All Questions
11 questions
5
votes
1
answer
297
views
Random walk with continuously distributed steps on [-1,1]
A simple random walk $S_n = X_1 +\cdots +X_n$, where $P(X_i = 1) = p \not = 0.5$ and $P(X_i=-1)= q \triangleq 1-p$, admits the following probability
$$P(S_n \textrm{ reaches } a \textrm{ before} -b) =...
- 108
5
votes
0
answers
485
views
Hierarchical Random Walk (also known as Hierarchical Hidden Markov Model)
Let us consider the following hierarchical (recursive) random walk model, which is also known as the hierarchical hidden Markov model in computer science (https://en.wikipedia.org/wiki/...
- 1,127
4
votes
3
answers
620
views
Averaging over random walk on binary lattice
I have a function $f$ defined over a bit vector of length $n$. Equivalently, this is a function defined on the set of integers $[0,\ldots,2^n-1]$. I would like to compute the mean or variance or some ...
- 757
4
votes
2
answers
255
views
The necessary sufficient condition for recurrence of a Markovian random walk
Suppose $\sigma_{1},\sigma_{2},...$are i.i.d random variables.$S_{0}=0$. Define $S_{n}=S_{0}+\sum_{i=1}^{n}\sigma_{i}$, then ${S_{n}}$ is a Markovian random walk.
I want to figure out the necessary ...
- 41
2
votes
1
answer
847
views
Probability that a symmetric random walk returns to $0$ exactly $k$ times in $2n$ steps
I'm trying to find a formula to find the probability of exactly k returns in 2n steps of a symmetric random walk. More specifically, I am trying to show that the probability of 2 returns is exactly ...
- 21
2
votes
1
answer
421
views
Extending Wald's equation to two classes of i.d. random variables?
I try to adopt Wald's equation to a slightly more complex problem. In fact, after a full day, I found some solution now, but it has a confusing argument in the middle. Perhaps somebody can help me at ...
- 340
2
votes
1
answer
447
views
MCMC with progressive demollification of delta distributions
Edit: I simplified the example to a canonical case for clarity.
Given an integral $\int_{\Omega}{g(\mathbf{x})}$ with a well-posed integrand $g(\mathbf{x})$ defined on some multidimensional space $\...
1
vote
1
answer
385
views
How fast does this Gaussian random walk move away from the origin?
Suppose $z_i$ are IID zero-centered $d$-dimensional Gaussian random variables with unit-trace covariance $\Sigma$ and $g(z_i)$ is the sum of its components.
Consider the following random walk:
$$x_s=\...
- 2,242
1
vote
2
answers
772
views
Gibbs sampling step size
I have some data generated using MCMC methods and in particular Gibbs sampling. I computed the autocorrelation but I'm unsure how to determine how many samples to skip.
I'd like to determine that ...
- 87
1
vote
2
answers
302
views
how to derive stationary distribution of maximal entropy random walk
I was reading the paper 0810.4113v2, burda, which analyzed the stationary distribution maximal entropy random walk on the irregular lattice. I am confused on some of the steps.
Description:
The ...
- 211
0
votes
1
answer
160
views
Probability to cross an envelopp for 1D random walk?
Imagine we have an evolving sequence composed of 1 and -1 (ex: -1-11-111...) where the probability to get -1 or 1 is 1/2. n is the lengh of my sequence.
I can make an analogy with random walk: let ...
- 5