Questions tagged [pr.probability]
Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.
7 questions from the last 7 days
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Explosion of the moment of double stochastic exponential
We consider the stochastic system
$$\frac{dS_t}{S_t}=-R_t\,dW_t,$$
with
$$dR_t=-R_t\,dt-R_t\,dW_t, \quad R_0>0.$$
We conjecture, and would like to show that
$$\mathbb{E}[S_t^2]
=
S_0^2\,\mathbb{E}\...
- 696
1
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40
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Tail log-convexity of moments of an even Hermite polynomial of a Gaussian
Let $G\sim N(0,1)$ and let $\{\mathrm{He}_n\}_{n\ge 0}$ denote the probabilists' Hermite polynomials.
Let $H_n:=\mathrm{He}_n/\sqrt{n!}$ be the orthonormal version, so that
$\mathbb{E}[H_n(G)H_m(G)]=\...
- 73
7
votes
1
answer
261
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What is the value of two player Liar’s Dice?
Alice and Biboo play a game. Each privately rolls a fair $n$ sided die labelled with $\{0, ..., n-1\}$, visible only to themselves. Players take turns with Alice starting first. Alice starts by making ...
- 11.2k
2
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0
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91
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Concentration inequalities for a specific type of random variables
Consider dynamics on the time interval $[0, n]$, $n \in \mathbb{N}$, where we events (a birth) happen after independent and unit-exponentially distributed waiting times. Every time $t$ such a event ...
- 838
6
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1
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218
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A too good to be true moment inequality for empirical processes
I have a question regarding an inequality that I obtained which seems to be too good to be true.
Consider a sequence $(X_i)_{i\leq N}$ of independent and identically distributed r.v.s. with law $\mu$ ...
- 273
32
votes
2
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713
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Is the expected distance between two random interior points of a convex body always at most that of two random boundary points?
Let $K \subset \mathbb{R}^2$ be a convex body. Define two quantities:
Interior mean distance. Let $X, Y$ be independent and uniformly distributed in $K$. Set
$$\Delta(K) \;=\; \mathbb{E}\,\|X - Y\|.$$...
- 1,012
13
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2
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256
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Behavior of certain random products of power series
Let $\varepsilon_1, \varepsilon_2, \cdots$ be independent random
variables taking the values $\pm 1$ with probability $1/2$ each. What
can be said about the coefficients $a_k$ of the power series ...
- 54.1k