-
作者：Da Prato, G.; Flandoli, F.; Priola, E.; Roeckner, M.
作者单位：Scuola Normale Superiore di Pisa; University of Pisa; University of Turin; University of Bielefeld
摘要：We prove pathwise (hence strong) uniqueness of solutions to stochastic evolution equations in Hilbert spaces with merely measurable bounded drift and cylindrical Wiener noise, thus generalizing Veretennikov's fundamental result on R-d to infinite dimensions. Because Sobolev regularity results implying continuity or smoothness of functions do not hold on infinite-dimensional spaces, we employ methods and results developed in the study of Malliavin-Sobolev spaces in infinite dimensions. The pric...
-
作者：Conus, Daniel; Joseph, Mathew; Khoshnevisan, Davar
作者单位：Lehigh University; Utah System of Higher Education; University of Utah
摘要：We consider a nonlinear stochastic heat equation at partial derivative(t)u = 1/2 partial derivative(xx)u + sigma(u)partial derivative W-xt, where partial derivative(xt) W denotes space time white noise and sigma : R -> R is Lipschitz continuous. We establish that, at every fixed time t > 0, the global behavior of the solution depends in a critical manner on the structure of the initial function u(0): under suitable conditions on u(0) and sigma, sup(x is an element of R)u(t)(x) is a.s. finite w...
-
作者：Oliveira, Roberto Imbuzeiro
作者单位：Instituto Nacional de Matematica Pura e Aplicada (IMPA)
摘要：We prove an upper bound for the epsilon-mixing time of the symmetric exclusion process on any graph G, with any feasible number of particles. Our estimate is proportional to T-RW(G) ln(vertical bar V vertical bar/epsilon), where vertical bar V vertical bar is the number of vertices in G, and T-RW(G) is the 1/4-mixing time of the corresponding single-particle random walk. This bound implies new results for symmetric exclusion on expanders, percolation clusters, the giant component of the Erdos-...
-
作者：Bayati, Mohsen; Gamarnik, David; Tetali, Prasad
作者单位：Stanford University; Massachusetts Institute of Technology (MIT); University System of Georgia; Georgia Institute of Technology
摘要：We establish the existence of free energy limits for several combinatorial models on Erdos-Renyi graph G(N, [cN]) and random r-regular graph G(N, r). For a variety of models, including independent sets, MAX-CUT, coloring and K-SAT, we prove that the free energy both at a positive and zero temperature, appropriately rescaled, converges to a limit as the size of the underlying graph diverges to infinity. In the zero temperature case, this is interpreted as the existence of the scaling limit for ...
-
作者：Chen, Wei-Kuo
作者单位：University of California System; University of California Irvine
摘要：We consider a spin system obtained by coupling two distinct Sherrington-Kirkpatrick (SK) models with the same temperature and external field whose Hamiltonians are correlated. The disorder chaos conjecture for the SK model states that the overlap under the corresponding Gibbs measure is essentially concentrated at a single value. In the absence of external field, this statement was first confirmed by Chatterjee [Disorder chaos and multiple valleys in spin glasses (2009) Preprint]. In the prese...
-
作者：del Barrio, Eustasio; Matran, Carlos
作者单位：Universidad de Valladolid
摘要：We consider the problem of optimal incomplete transportation between the empirical measure on an i.i.d. uniform sample on the d-dimensional unit cube [0, 1](d) and the true measure. This is a family of problems lying in between classical optimal transportation and nearest neighbor problems. We show that the empirical cost of optimal incomplete transportation vanishes at rate O-P(n(-1/d)), where n denotes the sample size. In dimension d >= 3 the rate is the same as in classical optimal transpor...
-
作者：Harnett, Daniel; Nualart, David
作者单位：University of Kansas
摘要：The purpose of this paper is to establish the convergence in law of the sequence of midpoint Riemann sums for a stochastic process of the form f'(W), where W is a Gaussian process whose covariance function satisfies some technical conditions. As a consequence we derive a change-of-variable formula in law with a second order correction term which is an Ito integral of f ''(W) with respect to a Gaussian martingale independent of W. The proof of the convergence in law is based on the techniques o...
-
作者：Barrieu, Pauline; El Karoui, Nicole
作者单位：University of London; London School Economics & Political Science; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
摘要：In this paper, we study the stability and convergence of some general quadratic semimartingales. Motivated by financial applications, we study simultaneously the semimartingale and its opposite. Their characterization and integrability properties are obtained through some useful exponential sub-martingale inequalities. Then, a general stability result, including the strong convergence of the martingale parts in various spaces ranging from H-1 to BMO, is derived under some mild integrability co...
-
作者：Emilia Caballero, M.; Perez Garmendia, Jose Luis; Uribe Bravo, Geronimo
作者单位：Universidad Nacional Autonoma de Mexico; Instituto Tecnologico Autonomo de Mexico; Universidad Nacional Autonoma de Mexico
摘要：Guided by the relationship between the breadth-first walk of a rooted tree and its sequence of generation sizes, we are able to include immigration in the Lamperti representation of continuous-state branching processes. We provide a representation of continuous-state branching processes with immigration by solving a random ordinary differential equation driven by a pair of independent Levy processes. Stability of the solutions is studied and gives, in particular, limit theorems (of a type prev...
-
作者：Mester, Peter
作者单位：Indiana University System; Indiana University Bloomington
摘要：We show by example that there is a Cayley graph, having two invariant random subgraphs X and Y, such that there exists a monotone coupling between them in the sense that X subset of Y, although no such coupling can be invariant. Here, invariant means that the distribution is invariant under group multiplications.
