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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Cumulative minimum of an Ornstein-Uhlenbeck process

Assume we generate a sample path $X_t$ from an Ornstein-Uhlenbeck distribution (i.e. a mean-reverting random walk), where $dX_t = −\rho(X_t − \mu)dt + \sigma dW_t$. For concreteness, take $\mu = 0$, ...
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Random walk question

here is the problem that I have been trying to do: N+1 plates are laid out around a circular dining table, and a hot cake is passed between them in the manner of a symmetric random walk: each time it ...
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counting combinations of {+1, -1} with constraints

I'm trying to count the number of ways of arranging a sequence of length $N+2L$ made of "$+1$" and "$-1$", with the following two conditions: 1) the total has to sum to $N$ 2) no partial sum is ...
56 views

Random sequence of $0$'s and $1$'s - what is the average 'in a row' succession

Let's say we create a sequence from coin tossing. Heads will be signified as $0$ and tails as $1$ Let's define $R$ as a successive elements(in the given sequence) of the same value. for example we ...
154 views

Proof that random walk visits zero infinitely many times

Since the Green function $G(x,1)=\sum\limits_{n\in \mathbb{N}_0}P(S_n=x), x\in\mathbb{Z}^d$ gives the expected number of visits to $x$ in a random walk, I'm asked to prove the following: I have to ...
If you do a random walk on an undirected, connected graph, is the stationary distribution for the probability that you have just traversed edge $e$ uniform over all edges no matter what the graph ...