-
作者：Ankirchner, Stefan; Fromm, Alexander; Kruse, Thomas; Popier, Alexandre
作者单位：Friedrich Schiller University of Jena; Justus Liebig University Giessen; Le Mans Universite
摘要：We consider a variant of the basic problem of the calculus of variations, where the Lagrangian is convex and subject to randomness adapted to a Brownian filtration. We solve the problem by reducing it, via a limiting argument, to an unconstrained control problem that consists in finding an absolutely continuous process minimizing the expected sum of the Lagrangian and the deviation of the terminal state from a given target position. Using the Pontryagin maximum principle, we characterize a sol...
-
作者：Arnaudon, M.; Del Moral, P.
作者单位：Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Centre National de la Recherche Scientifique (CNRS); Inria; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We propose a second order differential calculus to analyze the regularity and the stability properties of the distribution semigroup associated with McKean-Vlasov diffusions. This methodology provides second order Taylor type expansions with remainder for both the evolution semigroup as well as the stochastic flow associated with this class of nonlinear diffusions. Bismut-Elworthy-Li formulae for the gradient and the Hessian of the integro-differential operators associated with these expansion...
-
作者：Lopes, Fabio; Luczak, Malwina
作者单位：Universidad Tecnologica Metropolitana; University of Melbourne
摘要：We consider a simple Markov model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic SIS logistic epidemic process, and we assume that there is perfect cross-immunity between the two strains, that is, individuals infected by one are temporarily immune to re-infections and infections by the other. For the case where one strain is strictly stronger ...
-
作者：Durmus, Alain; Guillin, Arnaud; Monmarche, Pierre
作者单位：Universite Paris Saclay; Universite Clermont Auvergne (UCA); Sorbonne Universite; Universite Paris Cite
摘要：The Bouncy Particle Sampler (BPS) is a Monte Carlo Markov chain algorithm to sample from a target density known up to a multiplicative constant. This method is based on a kinetic piecewise deterministic Markov process for which the target measure is invariant. This paper deals with theoretical properties of BPS. First, we establish geometric ergodicity of the associated semi-group under weaker conditions than in (Ann. Statist. 47 (2019) 1268-1287) both on the target distribution and the veloci...
-
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, ...
-
作者：Lacker, Daniel
作者单位：Columbia University
摘要：This paper continues the study of the mean field game (MFG) conver- gence problem: In what sense do the Nash equilibria of n-player stochastic differential games converge to the mean field game as n -> infinity? Previous work on this problem took two forms. First, when the n-player equilibria are openloop, compactness arguments permit a characterization of all limit points of n-player equilibria as weak MFG equilibria, which contain additional randomness compared to the standard (strong) equil...
-
作者：Abbe, Emmanuel; Boix-Adsera, Enric
作者单位：Princeton University; Princeton University
摘要：This paper considers the problem of reconstructing n independent uni- form spins X-1,...,X-n living on the vertices of an n-vertex graph G, by observing their interactions on the edges of the graph. This captures instances of models such as (i) broadcasting on trees, (ii) block models, (iii) synchronization on grids, (iv) spiked Wigner models. The paper gives an upper bound on the mutual information between two vertices in terms of a bond percolation estimate. Namely, the information between t...
-
作者：Song, Jian; Yao, Jianfeng; Yuan, Wangjun
作者单位：Shandong University; University of Hong Kong; University of Hong Kong
摘要：In this article, we obtain an equation for the high-dimensional limit measure of eigenvalues of generalized Wishart processes, and the results are extended to random particle systems that generalize SDEs of eigenvalues. We also introduce a new set of conditions on the coefficient matrices for the existence and uniqueness of a strong solution for the SDEs of eigenvalues. The equation of the limit measure is further discussed assuming self-similarity on the eigenvalues.
-
作者：Ait-Sahalia, Yacine; Jacod, Jean
作者单位：Princeton University; Sorbonne Universite; Universite Paris Cite
摘要：Tick-by-tick asset price data exhibit a number of empirical regularities, including discreteness, long periods where prices are flat, periods of price moves of alternating plus and minus one tick, periods of rapid successive price moves of the same sign, and others. This paper proposes a framework to examine whether and how these microscopic features of the tick data are compatible with the typical macroscopic continuous-time models, based on Ito semimartingales, that are employed to represent...
-
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,...
