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A key result underlying the theory of MCMC is that any η-irreducible Markov chain having a transition density with respect to η and possessing a stationary distribution is automatically positive Harri...
In this paper a simple proof of the Chebyshev's inequality for random vectors obtained by Chen (arXiv:0707.0805v2, 2011) is obtained. This inequality gives a lower bound for the percentage of the popu...
We give a simple proof of Bell’s inequality in quantum mechanics which, in conjunction with experiments, demonstrates that the local hidden variables assumption is false. The proof sheds light on rela...
Audrey DeClue brought a sexual harassment claim against her employer arising out of her employer’s failure to provide her with private, or any, restroom facilities.1 She was the only woman working ...
Calvin Mackenzies book, Scandal Proof: Do Ethics Laws Make Government Ethical, is a concise, yet comprehensive, retrospective analysis of the development of ethical policy in the American federal ...
Chernoff proves an inequality using Hemite polynomials. Here we prove and generalize this inequality using Cauchy - Schwartz inequality and Fubini equality.
A detailed proof of Grabiner's theorem [I] on the exact asymptotics of the time to collision for n independent Brownian motions is given.
S. G. Bobkov and C. Houdré recently posed the following question on the Internet (Problem posed in Stochastic Analysis Digest no. 15 (9/15/1995)): Let X,Y be symmetric i.i.d. random variables such tha...
We show how the Clark-Ocone-Haussmann formula for Brownian motion on a compact Riemannian manifold put forward by S. Fang in his proof of the spectral gap inequality for the Ornstein-Uhlenbeck operato...
In 1981, J. Hawkes conjectured the exact form of the Hausdorff gauge function for the boundary of supercritical Galton-Watson trees under a certain assumption on the tail at infinity of the total mass...
We give a new representation of fractional Brownian motion with Hurst parameter $Hleqfrac{1}{2}$ using stochastic partial differential equations. This representation allows us to use the Markov proper...
A different but very short proof of a recent result of Khoshnevisan.
We give a simpler and shorter proof of Kesten's result for the probabilities with which a subordinator hits points.
In 1981, J. Hawkes conjectured the exact form of the Hausdorff gauge function for the boundary of supercritical Galton-Watson trees under a certain assumption on the tail at infinity of the total mass...

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