MathDB
simple random walk

Source: miklos schweitzer 2006 q11

September 4, 2021
probability and stats

Problem Statement

Let α\alpha be an irrational number, and denote F={(x,y)∈R2:y≥αx}F = \{ (x,y) \in R^2 : y \geq \alpha x \} as a closed half-plane bounded by a line. Let P(α,n)=P(X1,...,Xn∈F)P(\alpha,n) = P(X_1,...,X_n \in F), where XnX_n is a simple, symmetric random walk that starts at the origin and moves with probability 1/4 in each direction. Prove that P(α,n)P(\alpha,n) does not depend on α\alpha.
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