0
votes
0answers
29 views

Are there “necessary” conditions for a solution to the multivariate, truncated Hausdorff moment problem?

I am looking for NECESSARY conditions for a solution to the multivariate, truncated Hausdorff moment problem (i.e., conditions under which a given finite sequence of numbers is the sequence of first ...
4
votes
1answer
89 views

What is the right invariant $\sigma$-algebra for the Birkhoff ergodic theorem?

I have been reading stuff about ergodic theory, and I have encountered two versions of the involved "invariant sigma field". let the underlying probability space be $(\Omega,\mathcal{F},P)$, and let's ...
0
votes
0answers
72 views

Taylor expansion for a distribution function with a stochastic with a stochastic argument

I have seen the following and I am wondering why I can do this! Given two real valued random variables $X$ and $Y$ with finite variance. Than it holds that \begin{align*} P(X+Y \leq u)=P(X\leq ...
0
votes
1answer
42 views

Stochastic Processes Question

Give an example of a stochastic process $X_{n}$ that is not a Markov chain, such that $P_{y}(N(y)=\infty)=0$ but $E_{y}N(y)=\infty$
1
vote
1answer
98 views

Joint Convergence and Donsker's Theorem

I have a question about joint convergence results derived from an FCLT (i.e., a Functional Central Limit Theorem). To motivate my question, consider the following setup: Let $y_t$ be a random walk ...
2
votes
2answers
79 views

Question Regarding Poisson and probability.

i found this interesting question on the web but i am not quite sure if my solution is accurate. Honestly i would appreciate few opinions. Given Question: At a subway station, eastbound trains ...
2
votes
1answer
79 views

Readings necessary to understand Ito Integrals?

I searched for this question but couldn't find a direct answer. Basically I want to understand (and possibly compute some simple instances of) the Ito integral. I am coming from a physics background ...
2
votes
1answer
156 views

Is the expectation $E[\xi U'(\xi)]$ finite?

I encounter the following problem today. It seems a simple question. Let $U$ be a real function from $R^+\rightarrow \bar{R}$ satisfying the following conditions: (1) $U$ is concave, continuous, ...