-
作者：Seeger, Benjamin
作者单位：Universite PSL; Universite Paris-Dauphine; Universite PSL; College de France
摘要：The aim of this paper is to develop a general method for constructing approximation schemes for viscosity solutions of fully nonlinear pathwise stochastic partial differential equations, and for proving their convergence. Our results apply to approximations such as explicit finite difference schemes and Trotter-Kato type mixing formulas. The irregular time dependence disrupts the usual methods from the classical viscosity theory for creating schemes that are both monotone and convergent, an ob...
-
作者：Ascione, Giacomo; Pirozzi, Enrica; Toaldo, Bruno
作者单位：University of Naples Federico II; University of Turin
摘要：In this paper we characterize the distribution of the first exit time from an arbitrary open set for a class of semi-Markov processes obtained as time-changed Markov processes. We estimate the asymptotic behaviour of the survival function (for large t) and of the distribution function (for small t) and we provide some conditions for absolute continuity. We have been inspired by a problem of neurophyshiology and our results are particularly usefull in this field, precisely for the so-called Lea...
-
作者：Feray, Valentin
作者单位：University of Zurich
摘要：We use the recently developed method of weighted dependency graphs to prove central limit theorems for the number of occurrences of any fixed pattern in multiset permutations and in set partitions. This generalizes results for patterns of size 2 in both settings, obtained by Canfield, Janson and Zeil-berger and Chern, Diaconis, Kane and Rhoades, respectively.
-
作者：Mehri, Sima; Scheutzow, Michael; Stannat, Wilhelm; Zangeneh, Ian Z.
作者单位：Technical University of Berlin; Sharif University of Technology
摘要：Spatially structured neural networks driven by jump diffusion noise with monotone coefficients, fully path dependent delay and with a disorder parameter are considered. Well-posedness for the associated McKean-Vlasov equation and a corresponding propagation of chaos result in the infinite population limit are proven. Our existence result for the McKean-Vlasov equation is based on the Euler approximation that is applied to this type of equation for the first time.
-
作者：Majka, Mateusz B.; Mijatovic, Aleksandar; Szpruch, Lukasz
作者单位：University of Warwick; Alan Turing Institute; University of Edinburgh
摘要：Discrete time analogues of ergodic stochastic differential equations (SDEs) are one of the most popular and flexible tools for sampling high-dimensional probability measures. Non-asymptotic analysis in the L-2 Wasserstein distance of sampling algorithms based on Euler discretisations of SDEs has been recently developed by several authors for log-concave probability distributions. In this work we replace the log-concavity assumption with a log-concavity at infinity condition. We provide novel L...
-
作者：Possamai, Dylan; Touzi, Nizar; Zhang, Jianfeng
作者单位：Columbia University; Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique; University of Southern California
摘要：We consider zero-sum stochastic differential games with possibly path-dependent volatility controls. Unlike the previous literature, we allow for weak solutions of the state equation so that the players' controls are automatically of feedback type. In particular, we do not require the controls to be simple, which has fundamental importance for the possible existence of saddle-points. Under some restrictions, needed for the a priori regularity of the upper and lower value functions of the game,...
-
作者：Backhoff-Veraguas, Julio; Lacker, Daniel; Tangpi, Ludovic
作者单位：University of Vienna; Columbia University; Princeton University
摘要：We derive new limit theorems for Brownian motion, which can be seen as nonexponential analogues of the large deviation theorems of Sanov and Schilder in their Laplace principle forms. As a first application, we obtain novel scaling limits of backward stochastic differential equations and their related partial differential equations. As a second application, we extend prior results on the small-noise limit of the Schrodinger problem as an optimal transport cost, unifying the control-theoretic a...
-
作者：Mueller, Tobias; Penrose, Mathew D.
作者单位：University of Groningen; University of Bath
摘要：Let d >= 2. The Cheeger constant of a graph is the minimum surface-to-volume ratio of all subsets of the vertex set with relative volume at most 1/2. There are several ways to define surface and volume here: the simplest method is to count boundary edges (for the surface) and vertices (for the volume). We show that for a geometric (possibly weighted) graph on n random points in a d-dimensional domain with Lipschitz boundary and with distance parameter decaying more slowly (as a function of n) ...
-
作者：Nutz, Marcel; San Martin, Jaime; Tan, Xiaowei
作者单位：Columbia University; Columbia University; Universidad de Chile; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
摘要：We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of n-player equilibria converges to it as n -> infinity. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are limit points of n-player equilibria, but we also exhibit a remarkable class of mean field equilibria that are not lim...
-
作者：Mostovyi, Oleksii; Sirbu, Mihai
作者单位：University of Connecticut; University of Texas System; University of Texas Austin
摘要：We consider the problem of optimal consumption from labor income and investment in a general incomplete semimartingale market. The economic agent cannot borrow against future income, so the total wealth is required to be positive at (all or some) previous times. Under very general conditions, we show that an optimal consumption and investment plan exists and is unique, and provide a dual characterization in terms of an optional strong supermartingale deflator and a decreasing part, which charg...
