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作者：Benes, Vaclav E.; Aitsgori, Georgy G.; Karatzas, Ioannis
作者单位：Columbia University
摘要：We consider stochastic control with discretionary stopping for the drift of a diffusion process over an infinite time horizon. The objective is to choose a control process and a stopping time to minimize the expectation of a convex terminal cost in the presence of a fixed operating cost and a control-dependent running cost per unit of elapsed time. Under appropriate conditions on the coefficients of the controlled diffusion, an optimal pair of control and stopping rules is shown to exist. More...
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作者：Blessing, Jonas; Kupper, Michael
作者单位：Swiss Federal Institutes of Technology Domain; ETH Zurich; University of Konstanz
摘要：Based on the Chernoff approximation, we provide a general approximation result for convex monotone semigroups which are continuous w.r.t. the mixed topology on suitable spaces of continuous functions. Starting with a family (I (t))t >= 0 of operators, the semigroup is constructed as the limit S(t)f := limn ->infinity I (t/n)n f and is uniquely determined by the time derivative I'(0)f for smooth functions. We identify explicit conditions for the generating family (I (t))t >= 0 that are transfer...
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作者：Hamaguchi, Yushi
作者单位：Kyoto University
摘要：We establish weak existence and uniqueness in law for stochastic Volterra equations (SVEs for short) with completely monotone kernels and nondegenerate noise under mild regularity assumptions. In particular, our results reveal the regularization-by-noise effect for SVEs with singular kernels, allowing for multiplicative noise with H & ouml;lder diffusion coefficients. In order to prove our results, we reformulate the SVE into an equivalent stochastic evolution equation (SEE for short) defined ...
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作者：Chlebicka, Iwona; Latuszynski, Krzysztof; Miasojedow, Blaej
作者单位：University of Warsaw; University of Warwick
摘要：Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational physics and statistical computing. Yet, their most fun- damental properties, such as relations between convergence characteristics of their various versions, are not well understood. In this paper we prove the solidarity principle of the spectral gap for the Gibbs sampler: if any of the random scan or d! deterministic scans has a spec- tral gap then all of them have. Our methods rely on geometric interpreta...
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作者：Bierme, Hermine; Desolneux, Agnes
作者单位：Universite de Tours; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Universite Paris Saclay
摘要：We are interested here in modeling and estimating the anisotropy of Gaussian random fields through the geometry of their excursion sets. In order to do this, we use Lipschitz-Killing curvatures of the level sets as functions of the levels and see them as generalized processes for which we are able to obtain a joint functional central limit theorem. For 2D and 3D stationary Gaussian fields we provide explicit formulas for the Lipschitz-Killing curvature densities. Then, we can deduce geometrica...
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作者：Xu, Hao; Zeng, Qiang
作者单位：University of Macau; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
摘要：We study the energy landscape near the ground state of a model of a single particle in a random potential with trivial topology. More precisely, we find the large-dimensional limit of the Hessian spectrum at the global minimum of the Hamiltonian XN(x) + mu 2 HxH2, x E RN, when mu is above the phase transition threshold so that the system has only one critical point. Here XN is a locally isotropic Gaussian random field. The same idea is also applied to study the more general model of elastic ma...
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作者：Bercu, Bernard; Bonnefont, Michel; Fredes, Luis; Richou, Adrien
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Bordeaux
摘要：Chatterjee and Diaconis have recently shown the asymptotic normality for the joint distribution of the number of descents and inverse descents in a random permutation. A noteworthy point of their results is that the asymptotic variance of the normal distribution is diagonal, which means that the number of descents and inverse descents are asymptotically uncorrelated. The goal of this paper is to go further in this analysis by proving a large deviation principle for the joint distribution. We s...
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作者：Trauthwein, Tara
作者单位：University of Oxford
摘要：We establish new explicit bounds on the Gaussian approximation of Poisson functionals based on novel estimates of moments of Skorohod integrals. Combining these with the Malliavin-Stein method, we derive bounds in the moment assumptions on add-one cost operators-thereby extending the results from (Last, Peccati and Schulte, 2016). Our paper also removes a redundant term from the bound in Kolmogorov distance and replaces a complicated term by a simpler one, without requiring additional assumpti...
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作者：Casanova, ADRIaN GONZaLEZ; Spano, Dario; Wilke-berenguer, Maite
作者单位：Arizona State University; Arizona State University-Tempe; University of Warwick; Humboldt University of Berlin
摘要：We analyse a family of two-types Wright-Fisher models with selection in a random environment and skewed offspring distribution. We provide a calculable criterion to quantify the impact of different shapes of selection on the fate of the weakest allele, and thus compare them. The main mathematical tool is duality, which we prove to hold, also in presence of random environment (quenched and in some cases annealed), between the population's allele frequencies and genealogy, both in the case of fi...
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作者：Anugu, Sumith Reddy; Pang, Guodong
作者单位：Rice University
摘要：We study the optimal scheduling problem for a Markovian multiclass queueing network with abandonment in the Halfin-Whitt regime, under the long run average (ergodic) risk sensitive cost criterion. The objective is to prove asymptotic optimality for the optimal control arising from the corresponding ergodic risk sensitive control (ERSC) problem for the limiting diffusion. In particular, we show that the optimal ERSC value associated with the diffusion-scaled queueing process converges to that o...
