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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：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：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：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...
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作者：Duffie, Darrell; Qiao, Lei; Sun, Yeneng
作者单位：Stanford University; Shanghai University of Finance & Economics; National University of Singapore
摘要：Continuous-time random matching with a large (continuum) population is widely exploited in the literature, but has not had a rigorous formulation, nor a demonstration of its key assumed properties. This paper provides the first probabilistic foundation for this approach by presenting a mathematical model of continuous-time random matching and showing its existence and properties. The agents' types, which can change due to random matching and random mutation, form a continuum of independent con...
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作者：Dianetti, Jodi
作者单位：University of Rome Tor Vergata
摘要：This paper studies multidimensional mean field games with common noise and the related system of McKean-Vlasov forward-backward stochastic differential equations deriving from the stochastic maximum principle. We first propose some structural conditions which are related to the submodularity of the underlying mean field game and are a sort of opposite version of the well known Lasry-Lions monotonicity. By reformulating the representative player minimization problem via the stochastic maximum p...
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作者：Armentano, Diego; Azais, Jean-m arc; Leon, Jose afael
作者单位：Universidad de la Republica, Uruguay; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universidad de la Republica, Uruguay
摘要：Let X() be a random field from R-D to R-d, where D >= d. We study the level set X-1(u), where u is an element of R-d. Specifically, we provide a weak condition for this level set to be rectifiable. Next, we establish the Kac-Rice formula to compute the (D-d)-dimensional Hausdorff measure. Our results extend previous work, particularly in the non-Gaussian case where we obtain a very general result. We conclude with several extensions and examples of applications, including functions of Gaussian...
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作者：Forien, Raphael; Pang, Guodong; Pardoux, Etienne; Zotsa-Ngoufack, Arsene-Brice
作者单位：INRAE; Rice University; Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
摘要：We study an individual-based stochastic epidemic model in which infected individuals become susceptible again, after each infection. In contrast to classical compartment models, after each infection, the infectivity is a random function of the time elapsed since infection. Similarly, recovered individuals become gradually susceptible after some time according to a random susceptibility function. We study the large population asymptotic behaviour of the model: we prove a functional law of large...
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作者：Athreya, Siva; Den Hollander, Frank; Rollin, Adrian
作者单位：Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru; Leiden University - Excl LUMC; Leiden University; National University of Singapore
摘要：In this paper we consider the two-type Moran model with N individuals. Each individual is assigned a resampling rate, drawn independently from a probability distribution P on R+, and a type, either 1 or 0. Each individual resamples its type at its assigned rate, by adopting the type of an individual drawn uniformly at random. Let Y-N (t) denote the empirical distribution of the resampling rates of the individuals with type 1 at time Nt. We show that if P has countable support and satisfies cer...
