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作者：Arapostathis, Ari; Biswas, Anup; Borkar, Vivek S.
作者单位：University of Texas System; University of Texas Austin; Indian Institute of Science Education & Research (IISER) Pune; Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Bombay
摘要：We consider a dynamical system with finitely many equilibria and perturbed by small noise, in addition to being controlled by an expensive control. The controlled process is optimal for an ergodic criterion with a running cost that consists of the sum of the control effort and a penalty function on the state space. We study the optimal stationary distribution of the controlled process as the variance of the noise becomes vanishingly small. It is shown that depending on the relative magnitudes ...
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作者：Ding, Jian; Shen, Jianfei
作者单位：University of Chicago
摘要：For a one-dimensional simple random walk (S-t), for each time t we say a site x is a favorite site if it has the maximal local time. In this paper, we show that with probability 1 three favorite sites occurs infinitely often. Our work is inspired by Toth [Ann. Probab. 29 (2001) 484-503], and disproves a conjecture of Erdos and Revesz [In Mathematical Structure-Computational Mathematics-Mathematical Modelling 2 (1984) 152-157] and of Toth [Ann. Probab. 29 (2001) 484-503].
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作者：Eskenazis, Alexandros; Nayar, Piotr; Tkocz, Tomasz
作者单位：Princeton University; University of Warsaw
摘要：A symmetric random variable is called a Gaussian mixture if it has the same distribution as the product of two independent random variables, one being positive and the other a standard Gaussian random variable. Examples of Gaussian mixtures include random variables with densities proportional to e(-vertical bar t vertical bar P )and symmetric p-stable random variables, where p is an element of (0, 2]. We obtain various sharp moment and entropy comparison estimates for weighted sums of independ...
