187 research outputs found
Long time asymptotics of a Brownian particle coupled with a random environment with non-diffusive feedback force
We study the long time behavior of a Brownian particle moving in an
anomalously diffusing field, the evolution of which depends on the particle
position. We prove that the process describing the asymptotic behaviour of the
Brownian particle has bounded (in time) variance when the particle interacts
with a subdiffusive field; when the interaction is with a superdiffusive field
the variance of the limiting process grows in time as t^{2{\gamma}-1}, 1/2 <
{\gamma} < 1. Two different kinds of superdiffusing (random) environments are
considered: one is described through the use of the fractional Laplacian; the
other via the Riemann-Liouville fractional integral. The subdiffusive field is
modeled through the Riemann-Liouville fractional derivative.Comment: 45 page
Markov semigroups with hypocoercive-type generator in Infinite Dimensions: Ergodicity and Smoothing
We start by considering infinite dimensional Markovian dynamics in R^m
generated by operators of hypocoercive type and for such models we obtain short
and long time pointwise estimates for all the derivatives, of any order and in
any direction, along the semigroup. We then look at infinite dimensional models
(in (Rm)^{Z ^d}) produced by the interaction of infinitely many finite
dimensional dissipative dynamics of the type indicated above. For these
infinite dimensional models we study finite speed of propagation of
information, well-posedness of the semigroup, time behaviour of the derivatives
and strong ergodicity problem
Uniform in time estimates for the weak error of the Euler method for SDEs and a Pathwise Approach to Derivative Estimates for Diffusion Semigroups
We present a criterion for uniform in time convergence of the weak error of
the Euler scheme for Stochastic Differential equations (SDEs). The criterion
requires i) exponential decay in time of the space-derivatives of the semigroup
associated with the SDE and ii) bounds on (some) moments of the Euler
approximation. We show by means of examples (and counterexamples) how both i)
and ii) are needed to obtain the desired result. If the weak error converges to
zero uniformly in time, then convergence of ergodic averages follows as well.
We also show that Lyapunov-type conditions are neither sufficient nor necessary
in order for the weak error of the Euler approximation to converge uniformly in
time and clarify relations between the validity of Lyapunov conditions, i) and
ii).
Conditions for ii) to hold are studied in the literature. Here we produce
sufficient conditions for i) to hold. The study of derivative estimates has
attracted a lot of attention, however not many results are known in order to
guarantee exponentially fast decay of the derivatives. Exponential decay of
derivatives typically follows from coercive-type conditions involving the
vector fields appearing in the equation and their commutators; here we focus on
the case in which such coercive-type conditions are non-uniform in space. To
the best of our knowledge, this situation is unexplored in the literature, at
least on a systematic level. To obtain results under such space-inhomogeneous
conditions we initiate a pathwise approach to the study of derivative estimates
for diffusion semigroups and combine this pathwise method with the use of Large
Deviation Principles.Comment: 47 pages and 9 figure
Acoustic study of the Compañía de Jesús church. Characterization by means of objective and subjective parameters
This work shows the objective results of the acoustic quality of the Compañia de Jesús Church in Cordoba, Argentina. The acoustics of this Temple, built by the Orden Jesuita (Jesuit Order) two centuries ago and declared a World Heritage Site by UNESCO in 2000, is currently considered optimal by musicians as well as general public. In the second half of XVI century, with the Catholic reform, the need for improved speech intelligibility was given priority, being the Jesuit one of the orders that gave most importance to the construction of their temples. This church has constructive and spatial characteristics consistent with those needs. With the purpose of carrying out the acoustic assessment of the precincts, a work methodology that allowed comparing the results obtained from objective measures was developed by means of implementation of field measurements and space modeling, with subjective appreciation results, by developing surveys, with the aim of characterizing acoustically the sound space. This paper shows the comparison between the subjective results and objective criteria, which allowed important conclusions on the acoustic behavior of the temple to be obtained. In this way interesting data were obtained in relation to the subjective response of the acoustics of the church
Some remarks on degenerate hypoelliptic Ornstein-Uhlenbeck operators
37 pages, 3 figuresInternational audienceWe study degenerate hypoelliptic Ornstein-Uhlenbeck operators in spaces with respect to invariant measures. The purpose of this article is to show how recent results on general quadratic operators apply to the study of degenerate hypoelliptic Ornstein-Uhlenbeck operators. We first show that some known results about the spectral and subelliptic properties of Ornstein-Uhlenbeck operators may be directly recovered from the general analysis of quadratic operators with zero singular spaces. We also provide new resolvent estimates for hypoelliptic Ornstein-Uhlenbeck operators. We show in particular that the spectrum of these non-selfadjoint operators may be very unstable under small perturbations and that their resolvents can blow-up in norm far away from their spectra. Furthermore, we establish sharp resolvent estimates in specific regions of the resolvent set which enable us to prove exponential return to equilibrium
Long-time behaviour of degenerate diffusions: UFG-type SDEs and time-inhomogeneous hypoelliptic processes
We study the long time behaviour of a large class of diffusion processes on
, generated by second order differential operators of (possibly)
degenerate type. The operators that we consider {\em need not} satisfy the
H\"ormander condition. Instead, they satisfy the so-called UFG condition,
introduced by Herman, Lobry and Sussman in the context of geometric control
theory and later by Kusuoka and Stroock, this time with probabilistic
motivations. In this paper we study UFG diffusions and demonstrate the
importance of such a class of processes in several respects: roughly speaking
i) we show that UFG processes constitute a family of SDEs which exhibit
multiple invariant measures and for which one is able to describe a systematic
procedure to determine the basin of attraction of each invariant measure
(equilibrium state). ii) We use an explicit change of coordinates to prove that
every UFG diffusion can be, at least locally, represented as a system
consisting of an SDE coupled with an ODE, where the ODE evolves independently
of the SDE part of the dynamics. iii) As a result, UFG diffusions are
inherently "less smooth" than hypoelliptic SDEs; more precisely, we prove that
UFG processes do not admit a density with respect to Lebesgue measure on the
entire space, but only on suitable time-evolving submanifolds, which we
describe. iv) We show that our results and techniques, which we devised for UFG
processes, can be applied to the study of the long-time behaviour of
non-autonomous hypoelliptic SDEs and therefore produce several results on this
latter class of processes as well. v) Because processes that satisfy the
(uniform) parabolic H\"ormander condition are UFG processes, our paper contains
a wealth of results about the long time behaviour of (uniformly) hypoelliptic
processes which are non-ergodic, in the sense that they exhibit multiple
invariant measures.Comment: 66 page
Bounding stationary averages of polynomial diffusions via semidefinite programming
We introduce an algorithm based on semidefinite programming that yields
increasing (resp. decreasing) sequences of lower (resp. upper) bounds on
polynomial stationary averages of diffusions with polynomial drift vector and
diffusion coefficients. The bounds are obtained by optimising an objective,
determined by the stationary average of interest, over the set of real vectors
defined by certain linear equalities and semidefinite inequalities which are
satisfied by the moments of any stationary measure of the diffusion. We
exemplify the use of the approach through several applications: a Bayesian
inference problem; the computation of Lyapunov exponents of linear ordinary
differential equations perturbed by multiplicative white noise; and a
reliability problem from structural mechanics. Additionally, we prove that the
bounds converge to the infimum and supremum of the set of stationary averages
for certain SDEs associated with the computation of the Lyapunov exponents, and
we provide numerical evidence of convergence in more general settings
Incompetents - Sterilization - Court of Equity Has Inherent Power to Exercise Mentally Retarded Individual\u27s Right to Sterilization - In re Grady, 85 N.J. 235, 426 A.2d 467 (1981).
Regulation of intraluteal production of prostaglandins
There is clear evidence for intraluteal production of prostaglandins (PGs) in numerous species and under a variety of experimental conditions. In general, secretion of PGs appears to be elevated in the early corpus luteum (CL) and during the period of luteolysis. Regulation of intraluteal PG production is regulated by a variety of factors. An autoamplification pathway in which PGF-2alpha stimulates intraluteal production of PGF-2alpha has been identified in a number of species. The mechanisms underlying this autoamplification pathway appear to differ by species with expression of Cyclooxygenase-2 (Cox-2) and activity of phospholipase A2 acting as important physiological control points. In addition, a number of other responses that are induced by PGF-2alpha (decreased luteal progesterone, increased endothelin-1, increased cytokines) also have been found to increase intraluteal PGF-2alpha production. Thus, regulation of intraluteal PG production may serve to initiate or amplify physiological signals to the CL and may be important in specific aspects of luteal physiology particularly during luteal regression
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