# 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.

6,449 questions
Filter by
Sorted by
Tagged with
6 views

### Existence of Gaussian random field with prescribed covariance

Suppose a function $G:\mathbb{R}^d\rightarrow\mathbb{R}$ is given. What are some necessary or sufficient conditions on $G$ for there to exist a probability space $(\Omega,\mathcal{F},\mathbb{P})$ and ...
83 views

### Self-avoiding walks on strips

A strip is a locally finite graph which admits a quasi-transitive (i.e. finitley many orbits on vertices) action of $\mathbb Z$. A self avoiding walk is a walk which visits no vertex more than once. ...
29 views

### Distribution of the error of random signals

The signal vector of a fixed length $n$ consists of letter A, B, C. The probability that A,B,C appear at each digits are equal to a third. And the signal at each digits are independent. After ...
40 views

### Probability convergence [closed]

I have a question . we define d(X,Y) = E[min(|X-Y|,1)] for X,Y belongs L^0(Omega,A,P) I know : X_n converges in probability towards X iif lim d(X_n,X=0) And I must to prove there exists a subsequence ...
83 views

### Projective limit of spaces of probability measures

Consider a projective system $\dots X_{n+1} \to X_n \to \dots \to X_1$ of completely regular Hausdorff spaces with projective limit $X$. Then the linking mappings $f_n$ induce a projective system (in ...
48 views

### Relaxing conditional independent assumption

Suppose we have random variables Y, D and X, where Y is independent of D conditional on X (Y⊥D|X). If there is another variable Z=f(X), where f(.) is a measurable real function, my question is: (1) ...
52 views

### Bounding $l^0$ norm of random quantity

There are many techniques in high dimensional probability for bounding quantities of the form $$\mathbf{E}( \sup_{s \in S} X_s )$$ where $\{ X_s \}$ are a family of random variables which are not ...