169 research outputs found
Hamilton Jacobi Bellman equations in infinite dimensions with quadratic and superquadratic Hamiltonian
We consider Hamilton Jacobi Bellman equations in an inifinite dimensional
Hilbert space, with quadratic (respectively superquadratic) hamiltonian and
with continuous (respectively lipschitz continuous) final conditions. This
allows to study stochastic optimal control problems for suitable controlled
Ornstein Uhlenbeck process with unbounded control processes
Differentiability of backward stochastic differential equations in Hilbert spaces with monotone generators
The aim of the present paper is to study the regularity properties of the
solution of a backward stochastic differential equation with a monotone
generator in infinite dimension. We show some applications to the nonlinear
Kolmogorov equation and to stochastic optimal control
Exponential Mixing for a Stochastic PDE Driven by Degenerate Noise
We study stochastic partial differential equations of the reaction-diffusion
type. We show that, even if the forcing is very degenerate (i.e. has not full
rank), one has exponential convergence towards the invariant measure. The
convergence takes place in the topology induced by a weighted variation norm
and uses a kind of (uniform) Doeblin condition.Comment: 10 pages, 1 figur
Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations
In this paper we study the following non-autonomous stochastic evolution
equation on a UMD Banach space with type 2,
{equation}\label{eq:SEab}\tag{SE} {{aligned} dU(t) & = (A(t)U(t) + F(t,U(t)))
dt + B(t,U(t)) dW_H(t), \quad t\in [0,T],
U(0) & = u_0. {aligned}. {equation}
Here are unbounded operators with domains
which may be time dependent. We assume that
satisfies the conditions of Acquistapace and Terreni. The
functions and are nonlinear functions defined on certain interpolation
spaces and is the initial value. is a cylindrical Brownian
motion on a separable Hilbert space .
Under Lipschitz and linear growth conditions we show that there exists a
unique mild solution of \eqref{eq:SEab}. Under assumptions on the interpolation
spaces we extend the factorization method of Da Prato, Kwapie\'n, and Zabczyk,
to obtain space-time regularity results for the solution of
\eqref{eq:SEab}. For Hilbert spaces we obtain a maximal regularity result.
The results improve several previous results from the literature.
The theory is applied to a second order stochastic partial differential
equation which has been studied by Sanz-Sol\'e and Vuillermot. This leads to
several improvements of their result.Comment: Accepted for publication in Journal of Evolution Equation
Large deviations principle for the invariant measures of the 2D stochastic Navier-Stokes equations on a torus
We prove here the validity of a large deviation principle for the family of invariant measures associated to a two dimensional Navier-Stokes equation on a torus, perturbed by a smooth additive noise
Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise
The Freidlin-Wentzell large deviation principle is established for the
distributions of stochastic evolution equations with general monotone drift and
small multiplicative noise. As examples, the main results are applied to derive
the large deviation principle for different types of SPDE such as stochastic
reaction-diffusion equations, stochastic porous media equations and fast
diffusion equations, and the stochastic p-Laplace equation in Hilbert space.
The weak convergence approach is employed in the proof to establish the Laplace
principle, which is equivalent to the large deviation principle in our
framework.Comment: 31 pages, published in Appl. Math. Opti
Adjoint bi-continuous semigroups and semigroups on the space of measures
For a given bi-continuous semigroup T on a Banach space X we define its
adjoint on an appropriate closed subspace X^o of the norm dual X'. Under some
abstract conditions this adjoint semigroup is again bi-continuous with respect
to the weak topology (X^o,X). An application is the following: For K a Polish
space we consider operator semigroups on the space C(K) of bounded, continuous
functions (endowed with the compact-open topology) and on the space M(K) of
bounded Baire measures (endowed with the weak*-topology). We show that
bi-continuous semigroups on M(K) are precisely those that are adjoints of a
bi-continuous semigroups on C(K). We also prove that the class of bi-continuous
semigroups on C(K) with respect to the compact-open topology coincides with the
class of equicontinuous semigroups with respect to the strict topology. In
general, if K is not Polish space this is not the case
Stochastic Reaction-diffusion Equations Driven by Jump Processes
We establish the existence of weak martingale solutions to a class of second
order parabolic stochastic partial differential equations. The equations are
driven by multiplicative jump type noise, with a non-Lipschitz multiplicative
functional. The drift in the equations contains a dissipative nonlinearity of
polynomial growth.Comment: See journal reference for teh final published versio
Electronic cigarette use in 12 European countries. Results from the TackSHS survey.
BACKGROUND: Limited data on electronic cigarette prevalence, patterns and settings of use are available from several European countries. METHODS: Within the TackSHS project, a face-to-face survey was conducted in 2017-2018 in 12 European countries (Bulgaria, England, France, Germany, Greece, Ireland, Italy, Latvia, Poland, Portugal, Romania and Spain). Overall, 11,876 participants, representative of the population aged â„15 years in each country, provided information on electronic cigarette. RESULTS: 2.4% (95% confidence interval, CI: 2.2-2.7) of the subjects (2.5% among men and 2.4% among women; 0.4% among never, 4.4% among current- and 6.5% among ex-smokers) reported current use of electronic cigarette, ranging from 0.6% in Spain to 7.2% in England. Of the 272 electronic cigarette users, 52.6% were dual users (i.e., users of both electronic and conventional cigarettes) and 58.8% used liquids with nicotine. In all, 65.1% reported using electronic cigarette in at least one indoor setting where smoking is forbidden, in particular in workplaces (34.9%), and bars and restaurants (41.5%). Multivariable logistic regression analysis showed that electronic cigarette use was lower among older individuals (p for trend <0.001) and higher among individuals with high level of education (p for trend 0.040). Participants from countries with higher tobacco cigarette prices more frequently reported electronic cigarette use (odds ratio 3.62; 95% CI: 1.80-7.30). CONCLUSIONS: Considering the whole adult population of these 12 European countries, more than 8.3 million people use electronic cigarettes. The majority of users also smoked conventional cigarettes, used electronic cigarettes with nicotine and consumed electronic cigarettes in smoke-free indoor areas
Numerical methods for stochastic partial differential equations with multiples scales
A new method for solving numerically stochastic partial differential
equations (SPDEs) with multiple scales is presented. The method combines a
spectral method with the heterogeneous multiscale method (HMM) presented in [W.
E, D. Liu, and E. Vanden-Eijnden, Comm. Pure Appl. Math., 58(11):1544--1585,
2005]. The class of problems that we consider are SPDEs with quadratic
nonlinearities that were studied in [D. Blomker, M. Hairer, and G.A. Pavliotis,
Nonlinearity, 20(7):1721--1744, 2007.] For such SPDEs an amplitude equation
which describes the effective dynamics at long time scales can be rigorously
derived for both advective and diffusive time scales. Our method, based on
micro and macro solvers, allows to capture numerically the amplitude equation
accurately at a cost independent of the small scales in the problem. Numerical
experiments illustrate the behavior of the proposed method.Comment: 30 pages, 5 figures, submitted to J. Comp. Phy
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