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作者：Sun, Wen
作者单位：Chinese Academy of Sciences; University of Science & Technology of China, CAS
摘要：A pathwise large deviation result is proved for the pure jump models of the k-nary interacting particle system introduced by Kolokoltsov (Markov Process. Related Fields 12 (2006) 95-138; Nonlinear Markov Processes and Kinetic Equations (2010) Cambridge Univ. Press) that generalize classical Boltzmann's collision model, Smoluchovski's coagulation model and many others. The upper bound is obtained by following the standard methods (KOV (Comm. Pure Appl. Math. 42 (1989) 115-137)) of using a proce...
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作者：Zhang, Xiaolong; Zhang, Xicheng
作者单位：Beijing Institute of Technology
摘要：In this paper we establish the optimal regularity estimates for the Cauchy problem of stochastic kinetic equations with random coefficients in anisotropic Besov spaces. As applications, we study the nonlinear filtering problem for a degenerate diffusion process, and obtain the existence and regularity of conditional probability densities under a few assumptions. Moreover, we also show the well-posedness for a class of super-linear growth stochastic kinetic equations driven by velocity-time whi...
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作者：Kifer, Yuri
作者单位：Hebrew University of Jerusalem
摘要：It is known since (Theory Probab. Appl. 11 (1966) 390-406) that the slow motion X-epsilon in the time-scaled multidimensional averaging setup dX(epsilon)(t)/dt = 1/epsilon B(X-epsilon(t), xi(t/epsilon(2))) +b(X-epsilon(t), xi(t/epsilon(2))), t is an element of [0, T] converges weakly as epsilon -> 0 to a diffusion process provided EB(x, xi(s)) 0 where xi is a sufficiently fast mixing stochastic process. In this paper we show that both X-epsilon and a family of diffusions Xi(epsilon) can be red...
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作者：Lacoin, Hubert; Yang, Shangjie
作者单位：Bar Ilan University
摘要：We consider the simple exclusion process in the integer segment [[1, N]] with k <= N/2 particles and spatially inhomogenous jumping rates. A particle at site x is an element of [[1, Nil jumps to site x - 1 (if x >= 2) at rate 1 - omega(x) and to site x + 1 (if x <= N 1) at rate omega(x) if the target site is not occupied. The sequence omega = (omega(x))(x is an element of Z) is chosen by IID sampling from a probability law whose support is bounded away from zero and one (in other words the ran...
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作者：Flammant, Lucas
作者单位：Universite Polytechnique Hauts-de-France; Centre National de la Recherche Scientifique (CNRS)
摘要：The Euclidean directed spanning forest is a random forest in Rd introduced by Baccelli and Bordenave in 2007 and we introduce and study here the analogous tree in the hyperbolic space. The topological properties of the Euclidean DSF have been stated for d = 2 and conjectured for d = 3 (see further): it should be a tree for d is an element of{2, 3} and a countable union of disjoint trees for d >= 4. Moreover, it should not contain bi-infinite branches whatever the dimension d. In this paper, we...
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作者：Wolfer, Geoffrey; Kontorovich, Aryeh
作者单位：RIKEN; Ben-Gurion University of the Negev
摘要：We show that the minimax sample complexity for estimating the pseudo spectral gap gamma(ps) of an ergodic Markov chain in constant multiplicative error is of the order of (Theta) over tilde (1/gamma(ps)pi(star)), where pi(star) is the minimum stationary probability, recovering the known bound in the reversible setting for estimating the absolute spectral gap (Hsu et al., Ann. Appl. Probab. 29 (2019) 2439-2480), and resolving an open problem of Wolfer and Kontorovich (In Proceedings of the Thir...
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作者：Ferrari, Patrik; Occelli, Alessandra
作者单位：University of Bonn; Universite d'Angers
摘要：This article studies several properties of the half-space last passage percolation, in particular the two-time covariance. We show that, when the two end-points are at small macroscopic distance, then the first-order correction to the covariance for the point-to-point model is the same as the one of the stationary model. In order to obtain the result, we first derive comparison inequalities of the last passage increments for different models. This is used to prove tightness of the point-to-poi...
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作者：Seddik, Mohamed El Amine; Guillaud, Maxime; Couillet, Romain
作者单位：Inria; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
摘要：Relying on random matrix theory (RMT), this paper studies asymmetric order-d spiked tensor models with Gaussian noise. Using the variational definition of the singular vectors and values of Lim (In Proc. IEEE International Workshop on Computational Advances in Multi -Sensor Adaptive Processing (2005) 129-132), we show that the analysis of the considered model boils down to the analysis of an equivalent spiked symmetric blockwise random matrix, that is constructed from contractions of the studi...
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作者：Friesen, Martin; Jin, Peng
作者单位：Dublin City University; Beijing Normal-Hong Kong Baptist University
摘要：The Volterra square-root process on R-+(m) is an affine Volterra process with continuous sample paths. Under a suitable integrability condition on the resolvent of the second kind associated with the Volterra convolution kernel, we establish the existence of limiting distributions. In contrast to the classical square-root diffusion process, here the limiting distributions may depend on the initial state of the process. Our result shows that the nonuniqueness of limiting distributions is closel...
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作者：Besancon, Eustache; Coutin, Laure; Decreusefond, Laurent; Moyal, Pascal
作者单位：IMT - Institut Mines-Telecom; Institut Polytechnique de Paris; Telecom Paris; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Lorraine
摘要：Continuous time Markov Chains, Hawkes processes and many other interesting processes can be described as a solution of stochastic differential equations driven by Poisson measures. Previous works, using the Stein's method, give the convergence rate of a sequence of renormalized Poisson measures toward the Brownian motion in several distances, constructed on the model of the Kantorovitch Rubinstein (or Wasserstein-1) distance. We show that many operations (like time change, convolution) on cont...
