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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：Pedrotti, Francesco
作者单位：Institute of Science & Technology - Austria
摘要：Contractive coupling rates have been recently introduced by Conforti as a and Poincar & eacute; inequality) for some classes of Markov chains. In this work, for most of the examples discussed by Conforti, we use contractive coupling rates to prove stronger inequalities, in the form of curvature lower bounds (in entropic and discrete Bakry-& Eacute;mery sense) and geodesic convexity of some entropic functionals. In addition, we recall and give straightforward generalizations of some notions of ...
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作者：Schweinsberg, Jason; Shuai, Yubo
作者单位：University of California System; University of California San Diego
摘要：Consider a birth and death process started from one individual in which each individual gives birth at rate lambda and dies at rate mu, so that the population size grows at rater = lambda - mu. Lambert (Theor. Popul. Biol. 122 (2018) 30-35) and Harris, Johnston, and Roberts (Ann. Appl. Probab. 30 (2020) 1368-1414) came up with methods for constructing the exact genealogy of a sample of size n taken from this population at time T. We use the construction of Lambert, which is based on the coales...
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作者：Borkar, Vivek; Chen, Shuhang; Devraj, Adithya; Kontoyiannis, Ioannis; Meyn, Sean
作者单位：Indian Institute of Technology System (IIT System); Indian Institute of Technology (IIT) - Bombay; State University System of Florida; University of Florida; Stanford University; University of Cambridge; State University System of Florida; University of Florida
摘要：The paper concerns the stochastic approximation recursion, theta n+1 = theta n + alpha n+1f (theta n, Phi n+1), n >= 0, where the estimates {theta n} evolve on Ilgd, and Phi := {Phi n} is a stochastic process on a general state space, satisfying a conditional Markov property that allows for parameter-dependent noise. In addition to standard Lipschitz assumptions and conditions on the vanishing step-size sequence, it is assumed that the associated mean flow ddt theta t =f(theta t) is globally a...
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作者：Caputo, Pietro; Labbe, Cyril; Lacoin, Hubert
作者单位：Roma Tre University; Universite Paris Cite; Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We investigate a quadratic dynamical system known as nonlinear recombinations. This system models the evolution of a probability measure over the Boolean cube, converging to the stationary state obtained as the product of the initial marginals. Our main result reveals a cutoff phenomenon for the total variation distance in both discrete and continuous time. Additionally, we derive the explicit cutoff profiles in the case of monochromatic initial distributions. These profiles are different in t...
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作者：Friz, Peter k.; Salkeld, William; Wagenhofer, Thomas
作者单位：Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics; University of Nottingham; Technical University of Berlin
摘要：We consider a class of stochastic processes with rough stochastic volatility, examples of which include the rough Bergomi and rough Stein-Stein model, that have gained considerable importance in quantitative finance. A basic question for such (non-Markovian) models concerns efficient numerical schemes. While strong rates are well understood (order H), we tackle here the intricate question of weak rates. Our main result asserts that the weak rate, for a reasonably large class of test function, ...
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作者：Han, Xiyue; Schied, Alexander
作者单位：University of Waterloo
摘要：Motivated by pathwise stochastic calculus, we say that continuous real-valued function x admits the roughness exponent R if the pth variation of x converges to zero for p > 1/R and to infinity for p < 1/R. In our main result, we provide a mild condition on the Faber-Schauder coefficients of x under which the roughness exponent exists and is given as the limit of the classical Gladyshev estimates R-n(x). This result can be viewed as a strong consistency result for the Gladyshev estimators in an...
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作者：Chen, Chenyang; Ge, Hao
作者单位：Peking University
摘要：We consider a stochastic interacting vortex system of N particles, approximating the vorticity formulation of the 2-D Navier-Stokes equation on a torus. The singular interaction kernel is given by the Biot-Savart law. Assuming only that the initial state has finite energy, we derive a sample-path large deviation principle for the empirical measure as the number of vortices tends to infinity. This contrasts with previous studies that require the initial state to have finite entropy. The rate fu...
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作者：Mossel, Elchanan; Niles-Weed, Jonathan; Sohn, Youngtak; Sun, Nike; Zadik, Ilias
作者单位：Massachusetts Institute of Technology (MIT); New York University; New York University
摘要：We connect the study of phase transitions in high-dimensional statistical inference to the study of threshold phenomena in random graphs. A major question in the study of the Erdos-R & eacute;nyi random graph G(n, p) is to understand the probability, as a function of p p, that G(n, p) contains a given subgraph H = H Hn Hn. This was studied for many specific examples of H H, starting with classical work of Erdos and R & eacute;nyi (1960). More recent work studies this question for general H H, ...
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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...
