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作者：Mendoza-Arriaga, Rafael; Linetsky, Vadim
作者单位：University of Texas System; University of Texas Austin; Northwestern University
摘要：The present paper introduces a jump-diffusion extension of the classical diffusion default intensity model by means of subordination in the sense of Bochner. We start from the bi-variate process (X, D) of a diffusion state variable X driving default intensity and a default indicator process D and time change it with a Levy subordinator T. We characterize the time-changed process (X-t(phi), D-t(phi)) = (X (T-t), D (T-t)) as a Markovian Ito semimartingale and show from the Doob-Meyer decompositi...
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作者：Faure, Mathieu; Schreiber, Sebastian J.
作者单位：Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite; Aix-Marseille Universite; University of California System; University of California Davis
摘要：We analyze quasi-stationary distributions {mu(epsilon)}(epsilon>0) of a family of Markov chains {X-epsilon}(epsilon>0) that are random perturbations of a bounded, continuous map F : M -> M, where M is a closed subset of R-k. Consistent with many models in biology, these Markov chains have a closed absorbing set M-0 subset of M such that F(M-0) = M-0 and F (M \ M-0) = M \ M-0. Under some large deviations assumptions on the random perturbations, we show that, if there exists a positive attractor...
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作者：Berestycki, Julien; Berestycki, Nathanael; Limic, Vlada
作者单位：Universite Paris Cite; Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); University of Cambridge; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
摘要：We describe a new general connection between Lambda-coalescents and genealogies of continuous-state branching processes. This connection is based on the construction of an explicit coupling using a particle representation inspired by the lookdown process of Donnelly and Kurtz. This coupling has the property that the coalescent comes down from infinity if and only if the branching process becomes extinct, thereby answering a question of Bertoin and Le Gall. The coupling also offers new perspect...
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作者：Butkovsky, Oleg
作者单位：Lomonosov Moscow State University; Technion Israel Institute of Technology
摘要：We establish subgeometric bounds on convergence rate of general Markov processes in the Wasserstein metric. In the discrete time setting we prove that the Lyapunov drift condition and the existence of a good d-small set imply subgeometric convergence to the invariant measure. In the continuous time setting we obtain the same convergence rate provided that there exists a good d-small set and the Douc-Fort-Guillin supermaffingale condition holds. As an application of our results, we prove that t...
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作者：Fedrizzi, Ennio
作者单位：Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Cite
摘要：We use the inverse scattering transform and a diffusion approximation limit theorem to study the stability of soliton components of the solution of the nonlinear Schrodinger and Korteweg-de Vries equations under random perturbations of the initial conditions: for a wide class of rapidly oscillating random perturbations this problem reduces to the study of a canonical system of stochastic differential equations which depends only on the integrated covariance of the perturbation. We finally stud...
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作者：Atar, Rami; Gurvich, Itai
作者单位：Technion Israel Institute of Technology; Northwestern University
摘要：We consider the problem of minimizing queue-length costs in a system with heterogenous parallel servers, operating in a many-server heavy-traffic regime with nondegenerate slowdown. This regime is distinct from the well-studied heavy traffic diffusion regimes, namely the (single server) conventional regime and the (many-server) Halfin-Whitt regime. It has the distinguishing property that waiting times and service times are of comparable magnitudes. We establish an asymptotic lower bound on the...
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作者：Fontes, L. R. G.; Gava, R. J.; Gayrard, V.
作者单位：Universidade de Sao Paulo; Universidade Federal de Sao Carlos; Aix-Marseille Universite; Centre National de la Recherche Scientifique (CNRS)
摘要：We introduce trap models on a finite volume k-level tree as a class of Markov jump processes with state space the leaves of that tree. They serve to describe the GREM-like trap model of Sasaki and Nemoto. Under suitable conditions on the parameters of the trap model, we establish its infinite volume limit, given by what we call a K-process in an infinite k-level tree. From this we deduce that the K-process also is the scaling limit of the GREM-like trap model on extreme time scales under a fin...
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作者：Faggionato, A.; Roberto, C.; Toninelli, C.
作者单位：Sapienza University Rome; Universite Paris Nanterre; Sorbonne Universite; Universite Paris Cite; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite
摘要：We consider one-dimensional hierarchical coalescence processes (in short HCPs) where two or three neighboring domains can merge. An HCP consists of an infinite sequence of stochastic coalescence processes: each process occurs in a different epoch and evolves for an infinite time, while the evolutions in subsequent epochs are linked in such a way that the initial distribution of epoch n + 1 coincides with the final distribution of epoch n. Inside each epoch a domain can incorporate one of its n...
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作者：Alexander, Kenneth S.; Zygouras, Nikos
作者单位：University of Southern California; University of Warwick
摘要：We study the path properties of a random polymer attracted to a defect line by a potential with disorder, and we prove that in the delocalized regime, at any temperature, the number of contacts with the defect line remains in a certain sense tight in probability as the polymer length varies. On the other hand we show that at sufficiently low temperature, there exists a.s. a subsequence where the number of contacts grows like the log of the length of the polymer.
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作者：Kang, Hye-Won; Kurtz, Thomas G.; Popovic, Lea
作者单位：University System of Ohio; Ohio State University; University of Wisconsin System; University of Wisconsin Madison; University of Wisconsin System; University of Wisconsin Madison; Concordia University - Canada
摘要：Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a combination of the two. Motivated by models with multiple time-scales arising in systems biology, we present a general approach to proving a central limit theorem capturing the fluctuations of the original model around the deterministic limit. The central limit the...
