-
作者：Claisse, Julien
作者单位：Institut Polytechnique de Paris; ENSTA Paris; Ecole Polytechnique
摘要：In this paper, we aim to develop the stochastic control theory of branching diffusion processes where both the movement and the reproduction of the particles depend on the control. More precisely, we study the problem of minimizing the expected value of the product of individual costs penalizing the final position of each particle. In this setting, we show that the value function is the unique viscosity solution of a nonlinear parabolic PDE, that is, the Hamilton-Jacobi-Bellman equation corres...
-
作者：El Euch, Omar; Rosenbaum, Mathieu
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique
摘要：Rough volatility models are known to reproduce the behavior of historical volatility data while at the same time fitting the volatility surface remarkably well, with very few parameters. However, managing the risks of derivatives under rough volatility can be intricate since the dynamics involve fractional Brownian motion. We show in this paper that surprisingly enough, explicit hedging strategies can be obtained in the case of rough Heston models. The replicating portfolios contain the underl...
-
作者：Eldan, Ronen; Gross, Renan
作者单位：Weizmann Institute of Science
摘要：We study the behavior of exponential random graphs in both the sparse and the dense regime. We show that exponential random graphs are approximate mixtures of graphs with independent edges whose probability matrices are critical points of an associated functional, thereby satisfying a certain matrix equation. In the dense regime, every solution to this equation is close to a block matrix, concluding that the exponential random graph behaves roughly like a mixture of stochastic block models. We...
-
作者：Beskos, Alexandros; Roberts, Gareth; Thiery, Alexandre; Pillai, Natesh
作者单位：University of London; University College London; University of Warwick; National University of Singapore; Harvard University
摘要：We study the asymptotic behaviour of the Random Walk Metropolis algorithm on ridged probability densities where most of the probability mass is distributed along some key directions. Such class of probability measures arise in various applied contexts including for instance Bayesian inverse problems where the posterior measure concentrates on a manifold when the noise variance goes to zero. When the target measure concentrates on a linear manifold, we derive analytically a diffusion limit for ...
-
作者：Cattiaux, Patrick; Delebecque, Fanny; Pedeches, Laure
作者单位：Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse
摘要：In this paper we revisit and generalize various stochastic models extending the deterministic Cucker-Smale model for self-organization. We study flocking and swarming properties. We show how these properties strongly depend on the structure and on the variance of the noise.
-
作者：Goldsheid, Ilya; Sodin, Sasha
作者单位：University of London; Queen Mary University London; Tel Aviv University
摘要：The eigenvalues of the Hatano-Nelson non-Hermitian Anderson matrices, in the spectral regions in which the Lyapunov exponent exceeds the non-Hermiticity parameter, are shown to be real and exponentially close to the Hermitian eigenvalues. This complements previous results, according to which the eigenvalues in the spectral regions in which the non-Hermiticity parameter exceeds the Lyapunov exponent are aligned on curves in the complex plane.
-
作者：Li, Xiaoou; Liu, Jingchen; Lu, Jianfeng; Zhou, Xiang
作者单位：University of Minnesota System; University of Minnesota Twin Cities; Columbia University; Duke University; Duke University; City University of Hong Kong
摘要：Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from imprecise measurement and intrinsic randomness. In this paper, we perform asymptotic rare-event analysis for such elliptic PDEs with random inputs. In particular, we consider the asymptotic regime that the noise level converges to zero suggesting that the system uncertainty is low, but does exist. We develop sharp approximations of the probability of a larg...
-
作者：Chatterjee, Sourav; Diaconis, Persi
作者单位：Stanford University
摘要：The goal of importance sampling is to estimate the expected value of a given function with respect to a probability measure v using a random sample of size n drawn from a different probability measure If the two measures mu and v are nearly singular with respect to each other, which is often the case in practice, the sample size required for accurate estimation is large. In this article, it is shown that in a fairly general setting, a sample of size approximately exp(D(v || mu)) is necessary a...
-
作者：Federico, Salvatore; Gozzi, Fausto
作者单位：University of Siena; Luiss Guido Carli University
摘要：Verification theorems are key results to successfully employ the dynamic programming approach to optimal control problems. In this paper, we introduce a new method to prove verification theorems for infinite dimensional stochastic optimal control problems. The method applies in the case of additively controlled Ornstein-Uhlenbeck processes, when the associated Hamilton-Jacobi-Bellman (HJB) equation admits a mild solution (in the sense of [J. Differential Equations 262 (2017) 3343-3389]). The m...
-
作者：Avena, Luca; Guldas, Hakan; van der Hofstad, Remco; den Hollander, Frank
作者单位：Leiden University - Excl LUMC; Leiden University; Eindhoven University of Technology
摘要：The mixing time of a random walk, with or without backtracking, on a random graph generated according to the configuration model on n vertices, is known to be of order log n. In this paper, we investigate what happens when the random graph becomes dynamic, namely, at each unit of time a fraction alpha(n) of the edges is randomly rewired. Under mild conditions on the degree sequence, guaranteeing that the graph is locally tree-like, we show that for every epsilon is an element of (0, 1) the eps...
