1,720,972 research outputs found
Pathwise optimality for benchmark tracking
No full textWe consider the problem of investing in a portfolio in order to track or "beat" a given benchmark. We study this problem from the point of view of almost sure/pathwise optimality. We first obtain a control that is optimal in the mean and this control is then shown to be also pathwise optimal. The standard Merton model leads to lognormality of the value process so that it does not possess the required ergodic properties. We obtain ergodicity by transforming the process so that it remains bounded thereby using a method that can be related to a random time change. We furthermore describe a general approach to solve the Hamilton-Jacobi-Bellman equation corresponding to the given problem setup
Logarithmic Sobolev Inequality for Zero-Range Dynamics: independence of the particle number
No full textWe prove that the logarithmic-Sobolev constant for Zero-Range Processes in a box of diameter L may depend on L but not on the number of particles. This is a first, but relevant and quite technical step, in the proof that this logarithmic-Sobolev constant grows as the square of L, that is presented in a forthcoming paper
Entropy decay for interacting systems via the Bochner-Bakry-Émery approach
Full text linkWe obtain estimates on the exponential rate of decay of the relative entropy from
equilibrium for Markov processes with a non-local infinitesimal generator. We adapt some of the
ideas coming from the Bakry-Emery approach to this setting. In particular, we obtain volume-
independent lower bounds for the Glauber dynamics of interacting point particles and for various
classes of hardcore models
Pathwise optimality in stochastic control
No full textWe introduce a notion of pathwise optimality for stochastic control problems over an infinite time horizon, and give sufficient conditions for the existence of pathwise optimal controls. We analyze both diffusion processes and processes with discrete state space
Logarithmic Sobolev inequality for zero range dynamics
No full textWe consider a system of interacting particles on a finite subset of diameter L of the d-dimensional integer lattice, and with zero-range interaction. Under mild technical conditions, we prove that the logarithmic-Sobolev constant grows as L^
Sampling from a Gibbs Measure with Pair Interaction by Means of PCA
Full text linkWe consider the problem of approximate sampling from the nite volume Gibbs
measure with a general pair interaction. We exhibit a parallel dynamics (Probabilistic
Cellular Automaton) which eciently implements the sampling. In this dynamics
the product measure that gives the new conguration in each site contains a term
that tends to favour the original value of each spin. This is the main ingredient that
allows one to prove that the stationary distribution of the PCA is close in total variation
to the Gibbs measure. The presence of the parameter that drives the "inertial"
term mentioned above gives the possibility to control the degree of parallelism of the
numerical implementation of the dynamics
Realizable monotonicity for continuous-time Markov processes
No full textInternational audienceWe formalize and analyze the notions of stochastic monotonicity and realizable mono-tonicity for Markov Chains in continuous-time, taking values in a finite partially ordered set. Similarly to what happens in discrete-time, the two notions are not equivalent. However, we show that there are partially ordered sets for which stochastic monotonicity and realizable monotonicity coincide in continuous-time but not in discrete-time
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Entropy inequalities for unbounded spin systems
Full text linkWe consider nonconservative, reversible spin systems, with unbounded discrete spins. We show that for a class of these dynamics in a high temperature regime, the relative entropy with respect to the equilibrium distribution decays exponentially in time, although the logarithmic-Sobolev inequality fails. To this end we prove a weaker modification of the logarithmic-Sobolev inequality
- …
