# Tagged Questions

For questions on random walks, a mathematical formalization of a path that consists of a succession of random steps.

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### Can someone help explain a proof from Feller Vol1 III.5?

One will need a copy of Feller's text (3rd edition) to answer this question. The proof I'm having difficulty with is Theorem 1, pages 84-85. When he discusses the r=1 case, he says ... "To the ...
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### Consequence of random walk with positive speed on a graph

Consider a random walk $X(n)$ on a vertex-transitive graph where the random walk has positive speed, i.e., $$\lim\limits_{n \rightarrow \infty} \frac{d(X(n), X(0))}{n}= \alpha>0$$ almost surely. ...
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### Expected time of reaching 0 of a simple symmetric random walk

Consider the symmetric, simple random walk on $S = \{0, 1, \ldots , k\}$ for $k \in \mathbb N$. Let $$T = \min \{ n \in \mathbb N_0|X_n = 0\}$$ be the first time where the process reaches $0$ and ...
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### 2d random walk on the nonnegative quadrant using martingale techniques

I know the basics of (discrete time) martingales, and I'd appreciate any help and suggestions on how to prove the following using martingale techniques. Let $Z_n$, $n\ge 0$ be a random walk on the ...
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### Probability that random walkers meet

I was wondering about a question about Random Walks. I came across various papers where the probability of 2 random walkers in 1 dimension and 2 dimension starting at the same point and returning to ...
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### Random walks : Hitting and recurrence Times relation

I have trouble understanding that how $$E\left[T_0|X_{0} = 0\right] = 1 + E[H_0|X_0=1]$$ where $T_0 = \inf\{n \geq 1:X_n = 0 \}$ and $H_A =\inf\{ n\geq 0: X_n \in A \}$. In other words $T_0$ is the ...
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### How to calculate the correlation coefficient of two independent random walks to demonstrate spurious regression?

I heard of non-stationary time series could result in spurious regression, so I want to know, as sample size goes to infinity, how to calculate the correlation coefficient of two descrete independent ...
Let's consider a random walk. We start on the tile $n_0$. For our $q$th step, if we're already on the tile $k$ then we have a probability $P_{q,k,p}$ to go to the tile $p$ with $p\in\mathbb{N}$. ...