178 research outputs found
Embedded antennas for signal-transmissive-walls in radio-connected low-energy urban buildings
The work presented in this thesis intends to develop and analyze two solutions to improve the 5G signal indoor coverage in the Finnish buildings. Two frequency ranges of the 5G spectrum are considered relevant, sub-6,GHz and ac{mmWave}. A through analysis is carried out, from the description to the simulation of the proposed solutions.Outgoin
Modeling and analysis of random and stochastic input flows in the chemostat model
In this paper we study a new way to model noisy input flows in the chemostat model, based on the Ornstein-Uhlenbeck process. We introduce a parameter β as drift in the Langevin equation, that allows to bridge a gap between a pure Wiener process, which is a common way to model random disturbances, and no noise at all. The value of the parameter β is related to the amplitude of the deviations observed on the realizations. We show that this modeling approach is well suited to represent noise on an input variable that has to take non-negative values for almost any time.European Commission (EC). Fondo Europeo de Desarrollo Regional (FEDER)Ministerio de Economía y Competitividad (MINECO). EspañaJunta de Andalucí
Stochastic Shell Models driven by a multiplicative fractional Brownian--motion
We prove existence and uniqueness of the solution of a stochastic
shell--model. The equation is driven by an infinite dimensional fractional
Brownian--motion with Hurst--parameter , and contains a
non--trivial coefficient in front of the noise which satisfies special
regularity conditions. The appearing stochastic integrals are defined in a
fractional sense. First, we prove the existence and uniqueness of variational
solutions to approximating equations driven by piecewise linear continuous
noise, for which we are able to derive important uniform estimates in some
functional spaces. Then, thanks to a compactness argument and these estimates,
we prove that these variational solutions converge to a limit solution, which
turns out to be the unique pathwise mild solution associated to the
shell--model with fractional noise as driving process.Comment: 23 page
Random attractors for stochastic evolution equations driven by fractional Brownian motion
The main goal of this article is to prove the existence of a random attractor
for a stochastic evolution equation driven by a fractional Brownian motion with
. We would like to emphasize that we do not use the usual
cohomology method, consisting of transforming the stochastic equation into a
random one, but we deal directly with the stochastic equation. In particular,
in order to get adequate a priori estimates of the solution needed for the
existence of an absorbing ball, we will introduce stopping times to control the
size of the noise. In a first part of this article we shall obtain the
existence of a pullback attractor for the non-autonomous dynamical system
generated by the pathwise mild solution of an nonlinear infinite-dimensional
evolution equation with non--trivial H\"older continuous driving function. In a
second part, we shall consider the random setup: stochastic equations having as
driving process a fractional Brownian motion with . Under a
smallness condition for that noise we will show the existence and uniqueness of
a random attractor for the stochastic evolution equation
Pathwise solutions and attractors for retarded SPDEs with time smooth diffusion coefficients
In this paper we study the longtime dynamics of mild solutions to retarded
stochastic evolution systems driven by a Hilbert-valued Brownian motion. As a
preparation for this purpose we have to show the existence and uniqueness of a
cocycle solution of such an equation. We do not assume that the noise is given
in additive form or that it is a very simple multiplicative noise. However, we
need some smoothing property for the coefficient in front of the noise. The
main idea of this paper consists of expressing the stochastic integral in terms
of non-stochastic integrals and the noisy path by using an integration by
parts. This latter term causes that in a first moment only a local mild
solution can be obtained, since in order to apply the Banach fixed point
theorem it is crucial to have the H\"older norm of the noisy path to be
sufficiently small. Later, by using appropriate stopping times, we shall derive
the existence and uniqueness of a global mild solution. Furthermore, the
asymptotic behavior is investigated by using the {\it Random Dynamical Systems
theory}. In particular, we shall show that the global mild solution generates a
random dynamical system that, under an appropriate smallness condition for the
time lag, have associated a random attractor
Stochastic lattice dynamical systems with fractional noise
This article is devoted to study stochastic lattice dynamical systems driven
by a fractional Brownian motion with Hurst parameter . First of
all, we investigate the existence and uniqueness of pathwise mild solutions to
such systems by the Young integration setting and prove that the solution
generates a random dynamical system. Further, we analyze the exponential
stability of the trivial solution
Existence of exponentially attracting stationary solutions for delay evolution equations
We consider the exponential stability of semilinear stochastic evolution equations with delays when zero is not a solution for these equations. We prove the existence of a non-trivial stationary solution exponentially stable, for which we use a general random fixed point theorem for general cocycles.
We also construct stationary solutions with the stronger property of attracting bounded sets uniformly, by means of the theory of random dynamical systems and their conjugation properties
Exponential stability of stochastic evolution equations driven by small fractional Brownian motion with Hurst parameter in
This paper addresses the exponential stability of the trivial solution of
some types of evolution equations driven by H\"older continuous functions with
H\"older index greater than . The results can be applied to the case of
equations whose noisy inputs are given by a fractional Brownian motion
with covariance operator , provided that and is
sufficiently small.Comment: 19 page
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