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作者：Bayraktar, Erhan; Qiu, Jinniao
作者单位：University of Michigan System; University of Michigan; University of Calgary
摘要：We solve the optimal control problem of a one-dimensional reflected stochastic differential equation, whose coefficients can be path dependent. The value function of this problem is characterized by a backward stochastic partial differential equation (BSPDE) with Neumann boundary conditions. We prove the existence and uniqueness of a sufficiently regular solution for this BSPDE, which is then used to construct the optimal feedback control. In fact, we prove a more general result: the existence...
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作者：Bierkens, Joris; Roberts, Gareth O.; Zitt, Pierre-Andre
作者单位：Delft University of Technology; University of Warwick; Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel
摘要：The zigzag process is a piecewise deterministic Markov process which can be used in a MCMC framework to sample from a given target distribution. We prove the convergence of this process to its target under very weak assumptions, and establish a central limit theorem for empirical averages under stronger assumptions on the decay of the target measure. We use the classical Meyn-Tweedie approach (Markov Chains and Stochastic Stability (2009) Cambridge Univ. Press; Adv. in Appl. Probab. 25 (1993) ...
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作者：Nadtochiy, Sergey; Shkolnikov, Mykhaylo
作者单位：Illinois Institute of Technology; Princeton University
摘要：We propose an interacting particle system to model the evolution of a system of banks with mutual exposures. In this model, a bank defaults when its normalized asset value hits a lower threshold, and its default causes instantaneous losses to other banks, possibly triggering a cascade of defaults. The strength of this interaction is determined by the level of the so-called noncore exposure. We show that, when the size of the system becomes large, the cumulative loss process of a bank resulting...
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作者：Nam, Danny; Nestoridi, Evita
作者单位：Princeton University
摘要：We study the cyclic adjacent transposition (CAT) shuffle of n cards, which is a systematic scan version of the random adjacent transposition (AT) card shuffle. In this paper, we prove that the CAT shuffle exhibits cutoff at n(3)/2 pi(2) log n, which concludes that it is twice as fast as the AT shuffle. This is the first verification of cutoff phenomenon for a time-inhomogeneous card shuffle.
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作者：Monter, Sergio A. Almada; Shkolnikov, Mykhaylo; Zhang, Jiacheng
作者单位：JP Morgan Chase & Company; Princeton University; Princeton University; Princeton University
摘要：In the seminal work (Stochastic Portfolio Theory: Stochastic Modelling and Applied Probability (2002) Springer), several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment decisions, a concise mathematical description of their dynamics has been missing. We fill this gap in the setting of rank-based models. The results are then used to study th...
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作者：Damron, Michael; Gravner, Janko; Junge, Matthew; Lyu, Hanbaek; Sivakoff, David
作者单位：University System of Georgia; Georgia Institute of Technology; University of California System; University of California Davis; Duke University; University of California System; University of California Los Angeles; University System of Ohio; Ohio State University
摘要：Place a car independently with probability p at each site of a graph. Each initially vacant site is a parking spot that can fit one car. Cars simultaneously perform independent random walks. When a car encounters an available parking spot it parks there. Other cars can still drive over the site, but cannot park there. For a large class of transitive and unimodular graphs, we show that the root is almost surely visited infinitely many times when p >= 1/2, and only finitely many times otherwise.
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作者：Gangopadhyay, Ujan; Maulik, Krishanu
作者单位：University of Southern California; Indian Statistical Institute; Indian Statistical Institute Kolkata
摘要：The stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and same is true for the drift. However, the specific application of urn models with random replacement matrices motivates us to consider stochastic approximation in a setup where both the step sizes and the drift are random, but the sequence is uniformly b...
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作者：Hobson, David G.; Norgilas, Dominykas
作者单位：University of Warwick
摘要：Beiglbock and Juillet (Ann. Probab. 44 (2016) 42-106) introduced the left-curtain martingale coupling of probability measures mu and nu and proved that, when the initial law mu is continuous, it is supported by the graphs of two functions. We extend the later result by constructing the generalised left-curtain martingale coupling and show that for an arbitrary starting law mu it is characterised by two appropriately defined lower and upper functions. As an application of this result, we derive...
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作者：Bresler, Guy; Nagaraj, Dheeraj
作者单位：Massachusetts Institute of Technology (MIT)
摘要：We develop a new technique, based on Stein's method, for comparing two stationary distributions of irreducible Markov chains whose update rules are close in a certain sense. We apply this technique to compare Ising models on d-regular expander graphs to the Curie-Weiss model (complete graph) in terms of pairwise correlations and more generally kth order moments. Concretely, we show that d-regular Ramanujan graphs approximate the kth order moments of the Curie-Weiss model to within average erro...
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作者：Jacob, Emmanuel; Linker, Amitai; Moerters, Peter
作者单位：Ecole Normale Superieure de Lyon (ENS de LYON); Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile; University of Cologne
摘要：We study the contact process in the regime of small infection rates on finite scale-free networks with stationary dynamics based on simultaneous updating of all connections of a vertex. We allow the update rates of individual vertices to increase with the strength of a vertex, leading to a fast evolution of the network. We first develop an approach for inhomogeneous networks with general kernel and then focus on two canonical cases, the factor kernel and the preferential attachment kernel. For...
