Questions tagged [random-walk]
For questions on random walks, a mathematical formalization of a path that consists of a succession of random steps.
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Is the average of two identically distributed bounded martingales distributed in the same way?
I have seen this question and think it's sufficiently different (and well ranking on google) than the one I'm asking that makes it worth posting.
Lets say you have a barrier reflecting martingale, of ...
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Optimal permutation of transition probabilities in random walk to minimize expected stopping time
Background
Consider the set of integers $\{1,\dots,n+1\}$ and a set of probabilities $p_1,\dots, p_n \in(0,1)$. We now define a random walk/Markov chain on these states via the following transition ...
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2D Modified Random Walk
A particle starts at the point (0,0). It can move +1 to the right with a probability $p$, it can move +1 up with a probability $q$, and it can move diagonally up and to the right with probability $r$. ...
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Autocorrelation of p-values after $n$ observations
For $i = 1, 2, \dots$, let $X_i \sim N(0, 1)$ and $Y_i \sim N(0, 1)$, with all observations independent of each other.
Suppose that after observing $X_1, \dots, X_n, Y_1, \dots, Y_n$ we calculate the ...
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Growth in sum-of-squares under random applications of $(a,b)\to (a+b/2,b-a/2)$ to $\{1\}^N$
A recent question considered the following problem: "Several (at least two) nonzero numbers are written on a board. One
may erase any two numbers, say $a$ and $b$, and then write the numbers
$a+\...
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Distribution of the maximum of a "bridge" random walk
I found a card problem in an old book that essentially boiled down to this question: Suppose we have a random walk $S_n = X_1 + X_2 + \ldots + X_n$ that starts at $0$, where $X_i \hspace{0.1cm}$ is $1$...
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Sufficient condition for matrix factorization as an undirected graph random walk matrix
Let $A$ be an $n\times n$ row-stochastic matrix.
Is there a sufficient condition for $A$ to be factorized as $D^{-1} W$, where $W$ is a symmetric adjacency matrix for a weighted graph and $D=W\mathbf{...
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Biased random walk with chance of staying in place
A random walk has
probability $x$ of moving $+1$,
a probability $y$ of moving $0$,
and a probability $z$ of moving $-1$.
The PMF for arriving at position $m$ after $n$ steps can be found by summing ...
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Random walk with indipendent but not identically distributed increments
Suppose $\{Z_i\}_{i=1,2, \ldots}$
are normally distributed (independent but not identically distributed) random variables with mean $\mu(y)>0$ and positive variance $\sigma^2(y)$. Therefore we ...
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Bounded random walk joint distribution
Let $(X_n)_{n\in\mathbb{N}}$ be a sequence of i.i.d. normally distributed random variable with zero mean and variance $\sigma^2$. Consider the bounded random walk $(S_n)_{n\in\mathbb{N}}$, defined ...
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Mean hitting time of position-dependent random walk
The question
I am interested in a continuous-time random walk on $K$ states, numbered $0$ to $(K - 1)$. For each $k$:
I call $p_k$ the transition rate from state $k$ to state $(k + 1)$;
I call $n_k$ ...
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Where will a Non-Symmetric Random Walk be after time=t?
I posted this question about ranking the final position of a symmetric random walk after $t$ steps in terms of likelihood: What is the 2nd most likely value of a Random Walk after time=t?
I am now ...
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What is the 2nd most likely value of a Random Walk after time=t?
Here is a math problem I was thought of the other day involving Random Walks:
Let $X_t$, $t \in \{0, 1, 2, ..., n\}$, be a (discrete time) stochastic process where $$X_t \in \{-1, +1\}$$ $$P(X_t = +1) ...
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probability of two confined randomly walking bodies overlapping
EDIT: I have tried to rephrase the problem, title, and context to my solution
I am wondering about expanding a problem I have to the continuous domain. The problem is defined as such:
Problem
Given $N$...
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Circular random walk to generate a Polygon
I am trying to generate a set of points distributed in such a way as to give a "rough circle" sort of shape. The points should not deviate too far from neighboring points, with larger jumps ...
