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作者：Kardaras, Constantinos
作者单位：University of London; London School Economics & Political Science
摘要：Stochastic integrals are defined with respect to a collection P = (P-i; i is an element of I) of continuous semimartingales, imposing no assumptions on the index set I and the subspace of R-I where P takes values. The integrals are constructed though finite-dimensional approximation, identifying the appropriate local geometry that allows extension to infinite dimensions. For local martingale integrators, the resulting space S(P) of stochastic integrals has an operational characterisation via a...
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作者：Prodhomme, A. drien; Strickler, Edouard
作者单位：Universite de Tours; Universite de Lorraine; Inria; Centre National de la Recherche Scientifique (CNRS)
摘要：We consider an epidemic SIS model described by a multitype birth-and-death process in a randomly switching environment. That is, the infection and cure rates of the process depend on the state of a finite Markov jump process (the environment), whose transitions also depend on the number of infectives. The total size of the population is constant and equal to some K is an element of N*, and the number of infectives vanishes almost surely in finite time. We prove that, as K -> infinity, the proc...
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作者：Stannat, Wilhelm; Wessels, Lukas
作者单位：Technical University of Berlin; University System of Georgia; Georgia Institute of Technology
摘要：Using a recently introduced representation of the second order adjoint state as the solution of a function-valued backward stochastic partial differential equation (SPDE), we calculate the viscosity super- and subdifferential of the value function evaluated along an optimal trajectory for controlled semilinear SPDEs. This establishes the well-known connection between Pontryagin's maximum principle and dynamic programming within the framework of viscosity solutions. As a corollary, we derive th...
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作者：Xu, Wei
作者单位：Beijing Institute of Technology
摘要：In this work, several convergence results are established for nearly critical self-excited systems in which event arrivals are described by multivariate marked Hawkes point processes. Under some mild high -frequency assumptions, the rescaled density process behaves asymptotically like a multi -type continuous -state branching process with immigration, which is the unique solution to a multi -dimensional stochastic differential equation with dynamical mechanism similar to that of multivariate H...
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作者：Itkin, David; Larsson, Martin
作者单位：Imperial College London; Carnegie Mellon University
摘要：We propose a unified approach to several problems in stochastic portfolio theory (SPT), which is a framework for equity markets with a large number d of stocks. Our approach combines open markets , where trading is confined to the top N capitalized stocks as well as the market portfolio consisting of all d assets, with a parametric family of models which we call hybrid Jacobi processes . We provide a detailed analysis of ergodicity, particle collisions, and boundary attainment, and use these r...
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作者：Cook, Nicholas A.; Dembo, Amir
作者单位：Duke University; Stanford University
摘要：We consider general exponential random graph models (ERGMs) where the sufficient statistics are functions of homomorphism counts for a fixed collection of simple graphs F-k. Whereas previous work has shown a degeneracy phenomenon in dense ERGMs, we show this can be cured by raising the sufficient statistics to a fractional power. We rigorously establish the naive mean-field approximation for the partition function of the corresponding Gibbs measures, and in case of ferromagnetic models with va...
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作者：Last, Guenter; Penrose, Mathew d.; Zuyev, Sergei
作者单位：Helmholtz Association; Karlsruhe Institute of Technology; University of Bath; Chalmers University of Technology
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作者：Kazeykina, Anna; Ren, Zhenjie; Tan, Xiaolu; Yang, Junjian
作者单位：Universite Paris Saclay; Universite PSL; Universite Paris-Dauphine; Chinese University of Hong Kong; Technische Universitat Wien
摘要：We study the long time behavior of an underdamped mean -field Langevin (MFL) equation, and provide a general convergence as well as an exponential convergence rate result under different conditions. The results on the MFL equation can be applied to study the convergence of the Hamiltonian gradient descent algorithm for the overparametrized optimization. We then provide some numerical examples of the algorithm to train a generative adversarial network (GAN).
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作者：Chong, Carsten H.; Hoffmann, Marc; Liu, Yanghui; Rosenbaum, Mathieu; Szymanski, Gregoire
作者单位：Hong Kong University of Science & Technology; Universite PSL; Universite Paris-Dauphine; City University of New York (CUNY) System; Baruch College (CUNY); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：In recent years, there has been a substantive interest in rough volatility models. In this class of models, the local behavior of stochastic volatility is much more irregular than semimartingales and resembles that of a fractional Brownian motion with Hurst parameter H < 0.5. In this paper, we derive a consistent and asymptotically mixed normal estimator of H based on high-frequency price observations. In contrast to previous works, we work in a semiparametric setting and do not assume any a p...
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作者：Hasenpflug, Mareike; Rudolf, Daniel; Sprungk, Bjoern
作者单位：University of Passau; Technical University Freiberg
摘要：For l : R-d -> [0,infinity) we consider the sequence of probability measures (mu(n))(n is an element of N), where mu(n) is determined by a density that is proportional to exp(-nl). We allow for infinitely many global minimal points of l, as long as they form a finite union of compact manifolds. In this scenario, we show estimates for the p-Wasserstein convergence of (mu(n))(n is an element of N) to its limit measure. Imposing regularity conditions we obtain a speed of convergence of n(-1/(2p))...
