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作者：Friesen, Martin; Jin, Peng; Rudiger, Barbara
作者单位：University of Wuppertal; Shantou University
摘要：This work is devoted to the study of conservative affine processes on the canonical state space D = R-+(m) x R-n, where m + n > 0. We show that each affine process can be obtained as the pathwise unique strong solution to a stochastic equation driven by Brownian motions and Poisson random measures. Then we study the long-time behavior of affine processes, that is, we show that under first moment condition on the state-dependent and log-moment conditions on the state-independent jump measures, ...
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作者：Coghi, Michele; Deuschel, Jean-Dominique; Friz, Peter K.; Maurelli, Mario
作者单位：Technical University of Berlin; Technical University of Berlin; University of Milan
摘要：We take a pathwise approach to classical McKean-Vlasov stochastic differential equations with additive noise, as for example, exposed in Sznitmann (In Ecole D Ete de Probabilites de Saint-Flour XIX-1989 (1991) 165-251, Springer). Our study was prompted by some concrete problems in battery modelling (Contin. Mech. Thennodyn. 30 (2018) 593-628), and also by recent progrss on rough-pathwise McKean-Vlasov theory, notably Cass-Lyons (Proc. Lond. Math. Soc. (3) 110 (2015) 83-107), and then Bailleul,...
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作者：Mailler, Cecile; Villemonais, Denis
作者单位：University of Bath; Inria; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS)
摘要：Our main result is to prove almost-sure convergence of a stochastic-approximation algorithm defined on the space of measures on a noncompact space. Our motivation is to apply this result to measure-valued Polya processes (MVPPs, also known as infinitely-many Polya urns). Our main idea is to use Foster-Lyapunov type criteria in a novel way to generalize stochastic-approximation methods to measure-valued Markov processes with a noncompact underlying space, overcoming in a fairly general context ...
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作者：Mourrat, J-C
作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS)
摘要：We compute the large-scale limit of the free energy associated with the problem of inference of a finite-rank matrix. The method follows the principle put forward in Mourrat (2018) which consists in identifying a suitable Hamilton-Jacobi equation satisfied by the limit free energy. We simplify the approach of Mourrat (2018) using a notion of weak solution of the Hamilton-Jacobi equation which is more convenient to work with and is applicable whenever the nonlinearity in the equation is convex.
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作者：Junnila, Janne; Saksman, Eero; Webb, Christian
作者单位：Swiss Federal Institutes of Technology Domain; Ecole Polytechnique Federale de Lausanne; Norwegian University of Science & Technology (NTNU); Aalto University
摘要：In this article we study imaginary Gaussian multiplicative chaos-namely a family of random generalized functions which can formally be written as e(iX(x)), where X is a log-correlated real-valued Gaussian field on R-d, that is, it has a logarithmic singularity on the diagonal of its covariance. We study basic analytic properties of these random generalized functions, such as what spaces of distributions these objects live in, along with their basic stochastic properties, such as moment and tai...
