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作者：Xu, Lihu
作者单位：University of Macau
摘要：Let n is an element of N, let zeta(n,1), . . . , zeta(n,n) be a sequence of independent random variables with E zeta(n,i) = 0 and E vertical bar zeta(n,i)vertical bar < infinity for each i, and let mu be an alpha-stable distribution having characteristic function e(-vertical bar lambda vertical bar alpha) with alpha is an element of (1, 2). Denote S-n = zeta(n,1) + . . . + zeta(n,n) and its distribution by L (S-n), we bound the Wasserstein-1 distance of L(S-n) and mu essentially by an L-1 disc...
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作者：Bayraktar, Erhan; Budhiraja, Amarjit; Cohen, Asaf
作者单位：University of Michigan System; University of Michigan; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina School of Medicine; University of Haifa
摘要：We consider a large queueing system that consists of many strategic servers that are weakly interacting. Each server processes jobs from its unique critically loaded buffer and controls the rate of arrivals and departures associated with its queue to minimize its expected cost. The rates and the cost functions in addition to depending on the control action, can depend, in a symmetric fashion, on the size of the individual queue and the empirical measure of the states of all queues in the syste...
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作者：Yilmaz, Atilla; Zeitouni, Ofer
作者单位：Koc University; New York University; Weizmann Institute of Science
摘要：We consider a finite horizon stochastic optimal control problem for nearest-neighbor random walk {X-i} on the set of integers. The cost function is the expectation of the exponential of the path sum of a random stationary and ergodic bounded potential plus theta X-n. The random walk policies are measurable with respect to the random potential, and are adapted, with their drifts uniformly bounded in magnitude by a parameter delta is an element of [0, 1]. Under natural conditions on the potentia...
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作者：Burdzy, Krzysztof; Gauthier, Carl-Erik
作者单位：University of Washington; University of Washington Seattle
摘要：We consider random reflections (according to the Lambertian distribution) of a light ray in a thin variable width (but almost circular) tube. As the width of the tube goes to zero, properly rescaled angular component of the light ray position converges in distribution to a diffusion whose parameters (diffusivity and drift) are given explicitly in terms of the tube width.
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作者：Wang, Andi Q.; Kolb, Martin; Roberts, Gareth O.; Steinsaltz, David
作者单位：University of Oxford; University of Paderborn; University of Warwick
摘要：This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target density of interest. We also quantify the rate of convergence to quasi-stationarity by relating the killed diffusion to an appropriate Langevin diffusion. As an example, we consider in detail a killed Ornstein-Uhlenbeck process with Gaussian quasi-stationary d...
