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reviewed Close Show that the function $d(x, y)$ is a metric on the set $\mathbb R^2$ .
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reviewed Close company as none-binary tree
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comment Showing that lim sup of sum of iid binary variables $X_i$ with $P[X_i = 1] = P[X_i = -1] = 1/2$ is a.s. infinite
If you just want a hint, try to show the stronger claim that $P(\limsup \frac{S_n}{\sqrt{n}} = \infty) = 1$ using the 0-1 law and the CLT. If you want a full solution using this hint, I wrote it up here: math.stackexchange.com/questions/210131/…
Jan
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comment Distribution of integral of exponential Gaussian process?
As @Did said, this question is not currently well posed. Even if you mean that $X(t)$ is Brownian motion, this question is non-trivial. The distribution of $\int_0^T \text{exp}(u X(t))dt$ ($u$ real) has been studied by Matsumoto and Yor: arxiv.org/pdf/math/0511517.pdf I do not recall seeing anything for the complex case in any of their papers, but that is where I would start looking.
Jan
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reviewed Close Distribution of integral of exponential Gaussian process?
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reviewed Close Where is the border between functional analysis and real analysis?
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reviewed Close Property of ideal
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reviewed Close Analytic exponential function problem
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reviewed Close How to integrate this integral by contour integral?
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reviewed Close Prove that $\operatorname{Inn}(\operatorname{Aut}(G)) \cong \operatorname{Aut}(G)$
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reviewed Leave Open The limit of the alternating series $x - x^2 + x^4 - x^8 + {x^{16}}-\dotsb$ as $x \to 1$
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reviewed Close weakly convergence imply strong convergence when $ \|f_n\| \rightarrow \|f\| $ in $l^2([0,1])$?
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reviewed Leave Open Is $0$ an Infinitesimal?
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reviewed Close Show that two power series have the same radius of convergence