159 research outputs found
Stable dynamical systems under small perturbations
L'edifici fou construït el 1906.Primer pla, contrapicat, d'un edifici d'habitatges,
situat entre mitjeres.
Consta de planta baixa, cinc plantes pis. La coberta
és plana.
A la façana, hi destaca la gran profusió decorativa, de
formes vegetals i llenguatge modernista
Time irregularity of generalized Ornstein--Uhlenbeck processes
The paper is concerned with the properties of solutions to linear evolution
equation perturbed by cylindrical L\'evy processes. It turns out that
solutions, under rather weak requirements, do not have c\`adl\`ag modification.
Some natural open questions are also stated
Markovian Term Structure Models in Discrete Time
In this article we discuss Markovian term structure models in discrete time and with continuous state space. More precisely we are concerned with the structural properties of such models if one has the Markov property for a part of the forward curve. We investigate the two cases where these parts are either a true subset of the forward curve, including the short rate, or the entire forward curve. For the former case we give a sufficient condition for the term structure model to be affine. For the latter case we provide a version of the HJM [6] drift condition (see also [7]). Under a Gaussian assumption an HJM-Musiela [10] type equation is derive
On Minimum Energy Problems
A stochastic system described by a semilinear equation with a small noise is considered.
Under suitable hypotheses, the rate functionals for the family of distributions associated to the solution and the exit time and exit place of the solution are computed
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
Stabilising falling liquid film flows using feedback control
Falling liquid films become unstable due to inertial effects when the fluid layer is sufficiently thick or the slope sufficiently steep. This free surface flow of a single fluid layer has industrial applications including coating and heat transfer, which benefit from smooth and wavy interfaces, respectively. Here, we discuss how the dynamics of the system are altered by feedback controls based on observations of the interface height, and supplied to the system via the perpendicular injection and suction of fluid through the wall. In this study, we model the system using both Benney and weighted-residual models that account for the fluid injection through the wall. We find that feedback using injection and suction is a remarkably effective control mechanism: the controls can be used to drive the system towards arbitrary steady states and travelling waves, and the qualitative effects are independent of the details of the flow modelling. Furthermore, we show that the system can still be successfully controlled when the feedback is applied via a set of localised actuators and only a small number of system observations are available, and that this is possible using both static (where the controls are based on only the most recent set of observations) and dynamic (where the controls are based on an approximation of the system which evolves over time) control schemes. This study thus provides a solid theoretical foundation for future experimental realisations of the active feedback control of falling liquid films
Linear Operator Inequality and Null Controllability with Vanishing Energy for unbounded control systems
We consider linear systems on a separable Hilbert space , which are null
controllable at some time under the action of a point or boundary
control. Parabolic and hyperbolic control systems usually studied in
applications are special cases. To every initial state we
associate the minimal "energy" needed to transfer to in a time ("energy" of a control being the square of its norm). We
give both necessary and sufficient conditions under which the minimal energy
converges to for . This extends to boundary control
systems the concept of null controllability with vanishing energy introduced by
Priola and Zabczyk (Siam J. Control Optim. 42 (2003)) for distributed systems.
The proofs in Priola-Zabczyk paper depend on properties of the associated
Riccati equation, which are not available in the present, general setting. Here
we base our results on new properties of the quadratic regulator problem with
stability and the Linear Operator Inequality.Comment: In this version we have also added a section on examples and
applications of our main results. This version is similar to the one which
will be published on "SIAM Journal on Control and Optimization" (SIAM
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
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