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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
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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
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