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作者：Penda, S. Valere Bitseki; Delmas, Jean-Francois
作者单位：Universite Bourgogne Europe; Institut Polytechnique de Paris; Ecole Nationale des Ponts et Chaussees
摘要：Bifurcating Markov chains (BMC) are Markov chains indexed by a full binary tree representing the evolution of a trait along a population where each individual has two children. We provide a central limit theorem for general additive functionals of BMC, and prove the existence of three regimes. This corresponds to a competition between the reproducing rate (each individual has two children) and the ergodicity rate for the evolution of the trait. This is in contrast with the work of Guyon (Ann. ...
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作者：Li, Xue-Mei; Sieber, Julian
作者单位：Imperial College London
摘要：We prove a fractional averaging principle for interacting slow-fast systems. The mode of convergence is in Holder norm in probability. The main technical result is a quenched ergodic theorem on the conditioned fractional dynamics. We also establish geometric ergodicity for a class of fractional-driven stochastic differential equations, improving a recent result of Panloup and Richard.
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作者：Maillard, Pascal; Paquette, Elliot
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; McGill University
摘要：We consider a Markovian evolution on point processes, the psi -process, on the unit interval in which points are added according to a rule that depends only on the spacings of the existing point configuration. Having chosen a spacing, a new point is added uniformly within it. Building on previous work of the authors and of Junge, we show that the empirical distribution of points in such a process is always equidistributed under mild assumptions on the rule, generalizing work of Junge. A major ...
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作者：Kumar, Chaman; Neelima; Reisinger, Christoph; Stockinger, Wolfgang
作者单位：Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Roorkee; University of Delhi; University of Oxford
摘要：In this paper, we first establish well-posedness of McKean-Vlasov stochastic differential equations (McKean-Vlasov SDEs) with common noise, possibly with coefficients of super-linear growth in the state variable. Second, we present stable time-stepping schemes for this class of McKean-Vlasov SDEs. Specifically, we propose an explicit tamed Euler and tamed Milstein scheme for an interacting particle system associated with the McKean-Vlasov equation. We prove stability and strong convergence of ...
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作者：Yao, Jianfeng; Yuan, Wangjun
作者单位：The Chinese University of Hong Kong, Shenzhen; University of Hong Kong
摘要：In this article, we establish a limiting distribution for eigenvalues of a class of autocovariance matrices. The same distribution has been found in the literature for a regularized version of these autocovariance matrices. The original nonregularized autocovariance matrices are noninvertible, thus introducing supplementary difficulties for the study of their eigenvalues through Girko's Hermitization scheme. The key result in this paper is a new polynomial lower bound for a specific family of ...
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作者：Bierkens, Joris; Kamatani, Kengo; Roberts, Gareth O.
作者单位：Delft University of Technology; University of Osaka; University of Warwick
摘要：Piecewise deterministic Markov processes are an important new tool in the design of Markov chain Monte Carlo algorithms. Two examples of fundamental importance are the bouncy particle sampler (BPS) and the zig-zag process (ZZ). In this paper scaling limits for both algorithms are determined. Here the dimensionality of the space tends towards infinity and the target distribution is the multivariate standard normal distribution. For several quantities of interest (angular momentum, first coordin...
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作者：Eichinger, Katharina; Gnann, Manuel V.; Kuehn, Christian
作者单位：Universite PSL; Universite Paris-Dauphine; Delft University of Technology; Technical University of Munich
摘要：We investigate the stability of traveling-pulse solutions to the stochastic FitzHugh-Nagumo equations with additive noise. Special attention is given to the effect of small noise on the classical deterministically stable fast traveling pulse. Our method is based on adapting the velocity of the traveling wave by solving a scalar stochastic ordinary differential equation (SODE) and tracking perturbations to the wave meeting a system of a scalar stochastic partial differential equation (SPDE) cou...
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作者：Lacoin, Hubert; Yang, Shangjie
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We study the dynamical behavior of a one dimensional interface interacting with a sticky impenetrable substrate or wall. The interface is subject to two effects going in opposite directions. Contacts between the interface and the substrate are given an energetic bonus while an external force with constant intensity pulls the interface away from the wall. Our interface is modeled by the graph of a one-dimensional nearest-neighbor path on Z(+), starting at 0 and ending at 0 after 2N steps, with ...
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作者：Junge, Matthew; Lyu, Hanbaek
作者单位：City University of New York (CUNY) System; Baruch College (CUNY)
摘要：Ballistic annihilation is an interacting system in which particles placed throughout the real line move at preassigned velocities and annihilate upon colliding. The longstanding conjecture that in the symmetric three-velocity setting there exists a phase transition for the survival of middle-velocity particles was recently resolved by Haslegrave, Sidoravicius, and Tournier. We develop a framework based on a mass transport principle to analyze threevelocity ballistic annihilation with asymmetri...
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作者：Galeati, Lucio; Harang, Fabian A.
作者单位：University of Bonn; University of Oslo
摘要：We investigate the regularizing effect of certain additive continuous perturbations on SDEs with multiplicative fractional Brownian motion (fBm). Traditionally, a Lipschitz requirement on the drift and diffusion coefficients is imposed to ensure existence and uniqueness of the SDE. We show that suitable perturbations restore existence, uniqueness and regularity of the flow for the resulting equation, even when both the drift and the diffusion coefficients are distributional, thus extending the...
