 5:36 AM
A new tag created by nullUser.
0  I'm interested in a random walk on $\mathbb{Z}$ where $S_n = s_0 + X_1 + \cdots X_n$ with $X_i$ iid with $P(X_i = 0) = p$ and $P(X_i = -1) = P(X_i = +1) = q$. Let $\tau$ be the hitting time of $0$. I know that regardless of $s_0$, one has $P(\tau > k) \leq C/\sqrt{k}$ where $C$ may depend on \$p,... Hitting time
In the study of stochastic processes in mathematics, a hitting time (or first hit time) is the first time at which a given process "hits" a given subset of the state space. Exit times and return times are also examples of hitting times. == Definitions == Let T be an ordered index set such as the natural numbers, N, the non-negative real numbers, [0, +∞), or a subset of these; elements t ∈ T can be thought of as "times". Given a probability space (Ω, Σ, Pr) and a measurable state space S, let X : Ω × T → S be a stochastic process, and let A be a measurable subset of the state space S. Then the first... 5:59 AM
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Is functional analysis tag appropriate? No, I don't think (functional-analysis) tag is suitable for that question. I have removed the tag.