257 research outputs found
Approximating the coefficients in semilinear stochastic partial differential equations
We investigate, in the setting of UMD Banach spaces E, the continuous
dependence on the data A, F, G and X_0 of mild solutions of semilinear
stochastic evolution equations with multiplicative noise of the form dX(t) =
[AX(t) + F(t,X(t))]dt + G(t,X(t))dW_H(t), X(0)=X_0, where W_H is a cylindrical
Brownian motion on a Hilbert space H. We prove continuous dependence of the
compensated solutions X(t)-e^{tA}X_0 in the norms
L^p(\Omega;C^\lambda([0,T];E)) assuming that the approximating operators A_n
are uniformly sectorial and converge to A in the strong resolvent sense, and
that the approximating nonlinearities F_n and G_n are uniformly Lipschitz
continuous in suitable norms and converge to F and G pointwise. Our results are
applied to a class of semilinear parabolic SPDEs with finite-dimensional
multiplicative noise.Comment: Referee's comments have been incorporate
Conical square function estimates in UMD Banach spaces and applications to H-infinity functional calculi
We study conical square function estimates for Banach-valued functions, and
introduce a vector-valued analogue of the Coifman-Meyer-Stein tent spaces.
Following recent work of Auscher-McIntosh-Russ, the tent spaces in turn are
used to construct a scale of vector-valued Hardy spaces associated with a given
bisectorial operator (A) with certain off-diagonal bounds, such that (A) always
has a bounded (H^{\infty})-functional calculus on these spaces. This provides a
new way of proving functional calculus of (A) on the Bochner spaces
(L^p(\R^n;X)) by checking appropriate conical square function estimates, and
also a conical analogue of Bourgain's extension of the Littlewood-Paley theory
to the UMD-valued context. Even when (X=\C), our approach gives refined
(p)-dependent versions of known results.Comment: 28 pages; submitted for publicatio
Ergodicity, Decisions, and Partial Information
In the simplest sequential decision problem for an ergodic stochastic process
X, at each time n a decision u_n is made as a function of past observations
X_0,...,X_{n-1}, and a loss l(u_n,X_n) is incurred. In this setting, it is
known that one may choose (under a mild integrability assumption) a decision
strategy whose pathwise time-average loss is asymptotically smaller than that
of any other strategy. The corresponding problem in the case of partial
information proves to be much more delicate, however: if the process X is not
observable, but decisions must be based on the observation of a different
process Y, the existence of pathwise optimal strategies is not guaranteed.
The aim of this paper is to exhibit connections between pathwise optimal
strategies and notions from ergodic theory. The sequential decision problem is
developed in the general setting of an ergodic dynamical system (\Omega,B,P,T)
with partial information Y\subseteq B. The existence of pathwise optimal
strategies grounded in two basic properties: the conditional ergodic theory of
the dynamical system, and the complexity of the loss function. When the loss
function is not too complex, a general sufficient condition for the existence
of pathwise optimal strategies is that the dynamical system is a conditional
K-automorphism relative to the past observations \bigvee_n T^n Y. If the
conditional ergodicity assumption is strengthened, the complexity assumption
can be weakened. Several examples demonstrate the interplay between complexity
and ergodicity, which does not arise in the case of full information. Our
results also yield a decision-theoretic characterization of weak mixing in
ergodic theory, and establish pathwise optimality of ergodic nonlinear filters.Comment: 45 page
Regularity of Ornstein-Uhlenbeck processes driven by a L{\'e}vy white noise
The paper is concerned with spatial and time regularity of solutions to
linear stochastic evolution equation perturbed by L\'evy white noise "obtained
by subordination of a Gaussian white noise". Sufficient conditions for spatial
continuity are derived. It is also shown that solutions do not have in general
\cadlag modifications. General results are applied to equations with fractional
Laplacian. Applications to Burgers stochastic equations are considered as well.Comment: This is an updated version of the same paper. In fact, it has already
been publishe
Long-term exposure to air pollution and stroke incidence:A Danish Nurse cohort study
Ambient air pollution has been linked to stroke, but few studies have examined in detail stroke subtypes and confounding by road traffic noise, which was recently associated with stroke. Here we examined the association between long-term exposure to air pollution and incidence of stroke (overall, ischemic, hemorrhagic), adjusting for road traffic noise. In a nationwide Danish Nurse Cohort consisting of 23,423 nurses, recruited in 1993 or 1999, we identified 1,078 incident cases of stroke (944 ischemic and 134 hemorrhagic) up to December 31, 2014, defined as first-ever hospital contact. The full residential address histories since 1970 were obtained for each participant and the annual means of air pollutants (particulate matter with diameter < 2.5 μm and < 10 μm (PM2.5 and PM10), nitrogen dioxide (NO2), nitrogen oxides (NOx)) and road traffic noise were determined using validated models. Time-varying Cox regression models were used to estimate hazard ratios (HR) (95% confidence intervals (CI)) for the associations of one-, three, and 23-year running mean of air pollutants with stroke adjusting for potential confounders and noise. In fully adjusted models, the HRs (95% CI) per interquartile range increase in one-year running mean of PM2.5 and overall, ischemic, and hemorrhagic stroke were 1.12 (1.01–1.25), 1.13 (1.01–1.26), and 1.07 (0.80–1.44), respectively, and remained unchanged after adjustment for noise. Long-term exposure to ambient PM2.5 was associated with the risk of stroke independent of road traffic noise
On limit theorems for continued fractions
It is shown that for sums of functionals of digits in continued fraction
expansion the Kolmogorov-Feller weak laws of large numbers and the
Khinchine-L\'evy-Feller-Raikov characterization of the domain of attraction of
the normal law hold.Comment: 16 page
Lower-thermosphere–ionosphere (LTI) quantities: current status of measuring techniques and models
The lower-thermosphere-ionosphere (LTI) system consists of the upper atmosphere and the lower part of the ionosphere and as such comprises a complex system coupled to both the atmosphere below and space above. The atmospheric part of the LTI is dominated by laws of continuum fluid dynamics and chemistry, while the ionosphere is a plasma system controlled by electromagnetic forces driven by the magnetosphere, the solar wind, as well as the wind dynamo. The LTI is hence a domain controlled by many different physical processes. However, systematic in situ measurements within this region are severely lacking, although the LTI is located only 80 to 200 km above the surface of our planet. This paper reviews the current state of the art in measuring the LTI, either in situ or by several different remote-sensing methods. We begin by outlining the open questions within the LTI requiring high-quality in situ measurements, before reviewing directly observable parameters and their most important derivatives. The motivation for this review has arisen from the recent retention of the Daedalus mission as one among three competing mission candidates within the European Space Agency (ESA) Earth Explorer 10 Programme. However, this paper intends to cover the LTI parameters such that it can be used as a background scientific reference for any mission targeting in situ observations of the LTI.Peer reviewe
- …