# Tagged Questions

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### Comparing hitting time of two random walks

There are two random walks, $S^t_i=S^{t-1}_i+ X_i^t$ for $i=1,2$, $X^t_i$ i.i.d they have boundaries $h_1$ and $h_2$ respectively. I'm wondering if it's possible to calculate the probability that one ...
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### Invariant mesure of a reflected random walk

Let $(X_n), n \geq 0$ be a Reflected Random Walk defined by: $X_0 = 0$ and: $X_{n+1}=\max( 0 , X_n + \xi )$ $\xi$ is a random variable such that $P(\xi=a)=\theta$ and $P(\xi=-b)=1-\theta$ for a ...
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### Reflected random walk

Suppose that $X_n$ is a reflected (in 0) random walk with parameter $\theta$. So $X_{n+1}-X_n = 1$ with probability $\theta$ , and -1 with probability $1-\theta$ when $X_n \geq 1$, if $X_n=0$ then ...
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### Hitting time Distribution of a Gaussian Random Walk

I am trying to find out the exponential decay rate of the Probability $Pr(T>n)$ where $T$ is the first hitting time of a gaussian random walk with i.i.d random variables i.e. ...
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### Prove equilibrium theorem without irreducibility and aperiodicity

I have to solve the following question: Consider a random walk Markov chain on $S = \{1, 2, \ldots, 100\}$. If the chain is between 2 and 99, it selects one of the adjacent states with equal ...
### Absorption probability in 1D RW with asymmetric step sizes, $x<0$
What is the probability of absorption at $0$, as a function of position $x$, for a 1D random walk (on $\mathbb{Z}$) with asymmetric step sizes? For example, suppose that you can take two steps ...