-
作者：Popier, Alexandre; Zhou, Chao
作者单位：Le Mans Universite; National University of Singapore
摘要：In this work, we investigate an optimal liquidation problem under Knightian uncertainty. We obtain the value function and an optimal control characterised by the solution of a second-order BSDE with monotone generator and with a singular terminal condition.
-
作者：Bally, Vlad
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Inria
摘要：We deal with f(t)(dv), the solution of the homogeneous 2D Boltzmann equation without cutoff. The initial condition f(0)(dv) may be any probability distribution (except a Dirac mass). However, for sufficiently hard potentials, the semigroup has a regularization property (see Probab. Theory Related Fields 151 (2011) 659-704): f(t)(dv) = f(t)(v) dv for every t > 0. The aim of this paper is to give upper bounds for f(t)(v), the most significant one being of type f(t)(v) <= Ct(-eta)e(-vertical bar ...
-
作者：Jiang, Tiefeng
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Let x(1 ), . . . , x(n) be independent random vectors of a common p-dimensional normal distribution with population correlation matrix R-n . The sample correlation matrix (R) over cap (n) = ((r) over cap (ij))(pxp) is generated from x(1) , . . . . ,x(n) such that (r) over cap (ij) is the Pearson correlation coefficient between the ith column and the jth column of the data matrix (x(1 ), . . . , x(n))'. The matrix (R) over cap (n) is a popular object in multivariate analysis and it has many con...
-
作者：Kortchemski, Igor; Richier, Loic
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We are interested in the structure of large Bienayme-Galton-Watson random trees whose offspring distribution is critical and falls within the domain of attraction of a stable law of index alpha = 1. In stark contrast to the case alpha is an element of (1, 2], we show that a condensation phenomenon occurs: in such trees, one vertex with macroscopic degree emerges (see Figure 1). To this end, we establish limit theorems for centered downwards skip-free random walks whose steps are in the domain ...
-
作者：Hobson, David G.; Norgilas, Dominykas
作者单位：University of Warwick
摘要：Beiglbock and Juillet (Ann. Probab. 44 (2016) 42-106) introduced the left-curtain martingale coupling of probability measures mu and nu and proved that, when the initial law mu is continuous, it is supported by the graphs of two functions. We extend the later result by constructing the generalised left-curtain martingale coupling and show that for an arbitrary starting law mu it is characterised by two appropriately defined lower and upper functions. As an application of this result, we derive...
-
作者：Berger, Quentin; Torri, Niccolo
作者单位：Sorbonne Universite
摘要：We introduce a natural generalization of Hammersley's Last-Passage Percolation (LPP) called Entropy-controlled Last-Passage Percolation (E-LPP), where points can be collected by paths with a global (path-entropy) constraint which takes into account the whole structure of the path, instead of a local (1-Lipschitz) constraint as in Hammersley's LPP. Our main result is to prove quantitative tail estimates on the maximal number of points that can be collected by a path with entropy bounded by a pr...
-
作者：dos Reis, Goncalo; Salkeld, William; Tugaut, Julian
作者单位：University of Edinburgh; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
摘要：We show two Freidlin-Wentzell-type Large Deviations Principles (LDP) in path space topologies (uniform and Holder) for the solution process of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) using techniques which directly address the presence of the law in the coefficients and altogether avoiding decoupling arguments or limits of particle systems. We provide existence and uniqueness results along with several properties for a class of MV-SDEs having random coefficients and drifts of...
-
作者：Chassagneux, Jean-Francois; Crisan, Dan; Delarue, Francois
作者单位：Universite Paris Cite; Imperial College London; Universite Cote d'Azur
摘要：This paper is dedicated to the presentation and the analysis of a numerical scheme for forward-backward SDEs of the McKean-Vlasov type, or equivalently for solutions to PDEs on the Wasserstein space. Because of the mean field structure of the equation, earlier methods for classical forward- backward systems fail. The scheme is based on a variation of the method of continuation. The principle is to implement recursively local Picard iterations on small time intervals. We establish a bound for t...
-
作者：Davis, Erik; Sethuraman, Sunder
作者单位：University of Arizona
摘要：Given a cost functional F on paths gamma in a domain D subset of R-d, in the form 1 F(gamma) = integral(1)(0) f (gamma(t), gamma(t)) dt , it is of interest to approximate its minimum cost and geodesic paths. Let X-1,...X-n be points drawn independently from D according to a distribution with a density. Form a random geometric graph on the points where X-i and X-j are connected when 0 < vertical bar X-i - X-j vertical bar < epsilon, and the length scale epsilon = epsilon(n) vanishes at a suitab...
-
作者：Leite, Saul C.; Williams, Ruth J.
作者单位：Universidade Federal do ABC (UFABC); University of California System; University of California San Diego
摘要：Continuous-time Markov chain models are often used to describe the stochastic dynamics of networks of reacting chemical species, especially in the growing field of systems biology. These Markov chain models are often studied by simulating sample paths in order to generate Monte-Carlo estimates. However, discrete-event stochastic simulation of these models rapidly becomes computationally intensive. Consequently, more tractable diffusion approximations are commonly used in numerical computation,...
