-
作者：Kobylanski, Magdalena; Quenez, Marie-Claire; Rouy-Mironescu, Elisabeth
作者单位：Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Centre National de la Recherche Scientifique (CNRS); Universite Gustave-Eiffel; Centre National de la Recherche Scientifique (CNRS); Universite Paris Cite; Sorbonne Universite; 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 study the optimal multiple stopping time problem defined for each stopping time S by v(S) = ess sup(tau 1), ... , (tau d) (>=) (S) E[psi(tau(1), ... , tau(d))vertical bar F-S]. The key point is the construction of a new reward phi such that the value function v(S) also satisfies v(S) = ess sup(theta >= S) E[phi(theta)vertical bar F-S]. This new reward phi is not a right-continuous adapted process as in the classical case, but a family of random variables. For such a reward, we prove a new e...
-
作者：Fahim, Arash; Touzi, Nizar; Warin, Xavier
作者单位：Institut Polytechnique de Paris; Ecole Polytechnique; Electricite de France (EDF)
摘要：We consider the probabilistic numerical scheme for fully nonlinear partial differential equations suggested in [Comm. Pure Appl. Math. 60 (2007) 1081-1110] and show that it can be introduced naturally as a combination of Monte Carlo and finite difference schemes without appealing to the theory of backward stochastic differential equations. Our first main result provides the convergence of the discrete-time approximation and derives a bound on the discretization error in terms of the time step....
-
作者：Bramson, Maury
作者单位：University of Minnesota System; University of Minnesota Twin Cities
摘要：Join the shortest queue (JSQ) refers to networks whose incoming jobs are assigned to the shortest queue from among a randomly chosen subset of the queues in the system. After completion of service at the queue, a job leaves the network. We show that, for all nonidling service disciplines and for general interarrival and service time distributions, such networks are stable when they are subcritical. We then obtain uniform bounds on the tails of the marginal distributions of the equilibria for f...
-
作者：Kuna, Tobias; Lebowitz, Joel L.; Speer, Eugene R.
作者单位：University of Reading; Rutgers University System; Rutgers University New Brunswick
摘要：We give necessary and sufficient conditions for a pair of (generalized) functions rho(1)(r(1)) and rho(2) (r(1), r(2)), r(i) is an element of X, to be the density and pair correlations of some point process in a topological space X, for example, R(d), Z(d) or a subset of these. This is an infinite-dimensional version of the classical truncated moment problem. Standard techniques apply in the case in which there can be only a bounded number of points in any compact subset of X. Without this res...
-
作者：Constantin, Peter; Iyer, Gautam
作者单位：University of Chicago; Carnegie Mellon University
摘要：In this paper we derive a probabilistic representation of the deterministic 3-dimensional Navier-Stokes equations in the presence of spatial boundaries. The formulation in the absence of spatial boundaries was done by the authors in [Comm. Pure Appl. Math. 61 (2008) 330-345]. While the formulation in the presence of boundaries is similar in spirit, the proof is somewhat different. One aspect highlighted by the formulation in the presence of boundaries is the nonlocal, implicit influence of the...
-
作者：Brightwell, Graham; Luczak, Malwina
作者单位：University of London; London School Economics & Political Science
摘要：A causal set is a partially ordered set on a countably infinite ground-set such that each element is above finitely many others. A natural extension of a causal set is an enumeration of its elements which respects the order. We bring together two different classes of random processes. In one class, we are given a fixed causal set, and we consider random natural extensions of this causal set: we think of the random enumeration as being generated one point at a time. In the other class of proces...
-
作者：De Marco, Stefano
作者单位：Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris-Est-Creteil-Val-de-Marne (UPEC); Universite Gustave-Eiffel; Scuola Normale Superiore di Pisa
摘要：We study smoothness of densities for the solutions of SDEs whose coefficients are smooth and nondegenerate only on an open domain D. We prove that a smooth density exists on D and give upper bounds for this density. Under some additional conditions (mainly dealing with the growth of the coefficients and their derivatives), we formulate upper bounds that are suitable to obtain asymptotic estimates of the density for large values of the state variable (tail estimates). These results specify and ...
-
作者：Bertacchi, D.; Lanchier, N.; Zucca, F.
作者单位：University of Milano-Bicocca; Arizona State University; Arizona State University-Tempe; Polytechnic University of Milan
摘要：We introduce spatially explicit stochastic processes to model multispecies host-symbiont interactions. The host environment is static, modeled by the infinite percolation cluster of site percolation. Symbionts evolve on the infinite cluster through contact or voter type interactions, where each host may be infected by a colony of symbionts. In the presence of a single symbiont species, the condition for invasion as a function of the density of the habitat of hosts and the maximal size of the c...
-
作者：Fukasawa, Masaaki
作者单位：Japan Science & Technology Agency (JST); University of Osaka
摘要：Limit distributions for the error in approximations of stochastic integrals by Riemann sums with stochastic partitions are studied. The integrands and integrators are supposed to be one-dimensional continuous semimartingales. Lower bounds for asymptotic conditional variance of the error are given and effective discretization schemes which attain the bounds are explicitly constructed. Two examples of their applications are given; efficient delta hedging strategies under fixed or linear transact...
-
作者：Chatterjee, Sourav; Diaconis, Persi; Sly, Allan
作者单位：New York University; Stanford University; Microsoft
摘要：Large graphs are sometimes studied through their degree sequences (power law or regular graphs). We study graphs that are uniformly chosen with a given degree sequence. Under mild conditions, it is shown that sequences of such graphs have graph limits in the sense of Lovasz and Szegedy with identifiable limits. This allows simple determination of other features such as the number of triangles. The argument proceeds by studying a natural exponential model having the degree sequence as a suffici...
