Chris Janjigian
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 Feb 1 comment Prove that the limit in probability of normally distributed random variables is normally distributed, too @G.Sassatelli A sequence converges in probability to a random variable if and only if every subsequence has a further subsequence which converges to that random variable almost surely, so the questions are really the same. The answer in that question also only deals with limits in distribution, which is implied by convergence in probability. Jan 31 comment Prove that the limit in probability of normally distributed random variables is normally distributed, too math.stackexchange.com/questions/232540/… Jan 28 comment Prove that the stochastic process can not have continuous paths. It looks like you are missing a hypothesis. The constant function $W_t = 0$ is a solution with your current conditions. @Ant you do not need any assumptions more than the first and an assumption that the process is not constant. Jan 23 reviewed Close Martingale Poisson Jan 22 comment What is the use of moments in statistics @kjetilbhalvorsen This post is meant to be heuristic, so I was not terribly careful about assumptions. Nevertheless, under the assumption in paragraph 3 (finiteness of the moment generating function on a neighborhood of the origin), the distribution is determined by its moments. I am happy to defer to your better judgment about the quality of sample moments. Jan 22 awarded Enlightened Jan 21 reviewed Close Multiple integral $\idotsint_V dx_1 \, dx_2 \cdots dx_k$ where $\sum x_i \leq 1$ Jan 21 reviewed Close Show that the set of accumulation points of the sequence $a_n = \sin{n}$ is the closed interval $[-1, 1]$ Jan 20 reviewed Close How many five-digit numbers can be formed using digits 3,0,6,6,6? Jan 17 awarded Yearling Jan 15 comment Reference request: correlation and spectral analysis of stochastic processes You may want to look at Ash and Gardner's "Topics in Stochastic Processes." These topics are covered rigorously, though perhaps not in the level of generality you might want for all applications. Jan 5 awarded Custodian Jan 5 reviewed Approve Show that Hardy's inequality holds iff $f=0$ alomost everywhere Nov 18 awarded Popular Question Nov 10 revised Convergence of the fdds vs convergence in distribution in a function space fixed notation Nov 10 revised Convergence of the fdds vs convergence in distribution in a function space deleted 74 characters in body Nov 9 revised Convergence of the fdds vs convergence in distribution in a function space wording Nov 9 answered Convergence of the fdds vs convergence in distribution in a function space Nov 4 comment Tightness of a vector valued sequence of stochastic processes Tight in what space? If you mean the product of Skorokhod spaces (with the usual J1 topology), $D_{\mathbb{R}}[0,\infty)^2$, then yes. If you mean the Skorokhod space of the product (again, J1 topology), $D_{\mathbb{R}^2}[0,\infty)$, then no. Having one component be constant does not help if you mean the Skorokhod space of the product, but having one component be continuous does. Oct 18 revised Tightness of (sum of) elements of the Skorokhod space added 4 characters in body; added 62 characters in body