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作者：Arapostathis, Ari; Pang, Guodong; Sandric, Nikola
作者单位：University of Texas System; University of Texas Austin; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park; University of Zagreb
摘要：We study the ergodic properties of a class of multidimensional piecewise Ornstein-Uhlenbeck processes with jumps, which contains the limit of the queueing processes arising in multiclass many-server queues with heavy-tailed arrivals and/or asymptotically negligible service interruptions in the Halfin-Whitt regime as special cases. In these queueing models, the Ito equations have a piecewise linear drift, and are driven by either (1) a Brownian motion and a pure-jump Levy process, or (2) an ani...
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作者：Heydecker, Daniel
作者单位：University of Cambridge
摘要：We derive two estimates for the deviation of the N-particle, hard-spheres Kac process from the corresponding Boltzmann equation, measured in expected Wasserstein distance. Particular care is paid to the long-time properties of our estimates, exploiting the stability properties of the limiting Boltzmann equation at the level of realisations of the interacting particle system. As a consequence, we obtain an estimate for the propagation of chaos, uniformly in time and with polynomial rates, as so...
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作者：Davis, Erik; Sethuraman, Sunder
作者单位：University of Arizona
摘要：Given a cost functional F on paths gamma in a domain D subset of R-d, in the form 1 F(gamma) = integral(1)(0) f (gamma(t), gamma(t)) dt , it is of interest to approximate its minimum cost and geodesic paths. Let X-1,...X-n be points drawn independently from D according to a distribution with a density. Form a random geometric graph on the points where X-i and X-j are connected when 0 < vertical bar X-i - X-j vertical bar < epsilon, and the length scale epsilon = epsilon(n) vanishes at a suitab...
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作者：Leite, Saul C.; Williams, Ruth J.
作者单位：Universidade Federal do ABC (UFABC); University of California System; University of California San Diego
摘要：Continuous-time Markov chain models are often used to describe the stochastic dynamics of networks of reacting chemical species, especially in the growing field of systems biology. These Markov chain models are often studied by simulating sample paths in order to generate Monte-Carlo estimates. However, discrete-event stochastic simulation of these models rapidly becomes computationally intensive. Consequently, more tractable diffusion approximations are commonly used in numerical computation,...
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作者：Bartl, Daniel
作者单位：University of Konstanz
摘要：We consider the robust exponential utility maximization problem in discrete time: An investor maximizes the worst case expected exponential utility with respect to a family of nondominated probabilistic models of her endowment by dynamically investing in a financial market, and statically in available options. We show that, for any measurable random endowment (regardless of whether the problem is finite or not) an optimal strategy exists, a dual representation in terms of (calibrated) martinga...
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作者：Benaim, Michel; Strickler, Edouard
作者单位：University of Neuchatel
摘要：Let E be a finite set, {F-i}(i is an element of E) a family of vector fields on R-d leaving positively invariant a compact set M and having a common zero p is an element of M. We consider a piecewise deterministic Markov process (X, I) on M x E defined by (X)over dot(t)=F(I)t(X-t) where I is a jump process controlled by X: Pr(It+s = j vertical bar(X-u ,I-u)(u <= t)) = a(ij)(X-t)(s) + o(s) for i not equal j on {I-t=i}. We show that the behaviour of (X, I) is mainly determined by the behaviour o...
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作者：Peskir, Goran
作者单位：University of Manchester
摘要：We first show that a smooth fit between the value function and the gain function at the optimal stopping boundary for a two-dimensional diffusion process implies the absence of boundary's discontinuities of the first kind (the right-hand and left-hand limits exist but differ). We then show that the smooth fit itself is satisfied over the flat portion of the optimal stopping boundary arising from any of its hypothesised jumps. Combining the two facts we obtain that the optimal stopping boundary...
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作者：Blancas, Airam; Rogers, Tim; Schweinsberg, Jason; Siri-Jegousso, Arno
作者单位：Goethe University Frankfurt; University of Bath; University of California System; University of California San Diego; Universidad Nacional Autonoma de Mexico
摘要：The nested Kingman coalescent describes the ancestral tree of a population undergoing neutral evolution at the level of individuals and at the level of species, simultaneously. We study the speed at which the number of lineages descends from infinity in this hierarchical coalescent process and prove the existence of an early-time phase during which the number of lineages at time t decays as 2 gamma/ct(2), where c is the ratio of the coalescence rates at the individual and species levels, and t...
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作者：Bakhtin, Yuri; Pajor-Gyulai, Zsolt
作者单位：New York University
摘要：For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. Using Malliavin calculus tools, we obtain precise vanishing noise asymptotics for the tail of the exit time and for the exit distribution conditioned on atypically long exits.
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作者：Tsukuda, Koji
作者单位：University of Tokyo
摘要：The Ewens sampling formula was first introduced in the context of population genetics by Warren John Ewens in 1972, and has appeared in a lot of other scientific fields. There are abundant approximation results associated with the Ewens sampling formula especially when one of the parameters, the sample size n or the mutation parameter theta which denotes the scaled mutation rate, tends to infinity while the other is fixed. By contrast, the case that theta grows with n has been considered in a ...
