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Results tagged with random-walks
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user 8369
3
votes
1
answer
333
views
Maximizer of random walk with very small drift
This is an extended question based on
Large deviations for maximizer of random walk with drift.
Let $$S_k = X_1 + \ldots + X_k,$$ where $X_i$ are i.i.d. with mean $-\mu < 0$ and unit variance. Assume …
- 773
7
votes
0
answers
765
views
Calculate the expectation of the maximum of averaged random walks
Let $X_1, X_2, \ldots$ be iid random variables with bounded second moment. The question is to calculate the exact value of $$\mathbb{E} \max_{1 \le j < \infty} \frac{X_1 + \cdots + X_j}{j}.$$
Is ther …
- 773
10
votes
4
answers
664
views
The min of the mean of iid exponential variables
Let $X_1, \ldots, X_n, \ldots$ be iid exponential random variables with mean 1. It is well-known that $\min_{1\le j < \infty} \frac{X_1 + \cdots + X_j}{j}$ follows the uniform distribution U(0,1). Can …
- 773