103 research outputs found
Asymptotic behaviour of the density in a parabolic SPDE
Consider the density of the solution of a stochastic heat equation with small noise at a fixed , . In the paper we study the asymptotics of this density as the noise is vanishing. A kind of Taylor expansion in powers of the noise parameter is obtained. The coefficients and the residue of the expansion are explicitly calculated. In order to obtain this result some type of exponential estimates of tail probabilities of the difference between the approximating process and the limit one is proved. Also a suitable local integration by parts formula is developped.Malliavin Calculus, parabolic SPDE, large deviations, Taylor expansion of a density, exponential estimates of the tail probabilities, stochastic integration by parts formula
Non elliptic SPDEs and ambit fields: existence of densities
Relying on the method developed in [debusscheromito2014], we prove the
existence of a density for two different examples of random fields indexed by
(t,x)\in(0,T]\times \Rd. The first example consists of SPDEs with Lipschitz
continuous coefficients driven by a Gaussian noise white in time and with a
stationary spatial covariance, in the setting of [dalang1999]. The density
exists on the set where the nonlinearity of the noise does not vanish.
This complements the results in [sanzsuess2015] where is assumed to be
bounded away from zero. The second example is an ambit field with a stochastic
integral term having as integrator a L\'evy basis of pure-jump, stable-like
type.Comment: 23 page
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
Numerical Schemes for Rough Parabolic Equations
This paper is devoted to the study of numerical approximation schemes for a
class of parabolic equations on (0, 1) perturbed by a non-linear rough signal.
It is the continuation of [8, 7], where the existence and uniqueness of a
solution has been established. The approach combines rough paths methods with
standard considerations on discretizing stochastic PDEs. The results apply to a
geometric 2-rough path, which covers the case of the multidimensional
fractional Brownian motion with Hurst index H \textgreater{} 1/3.Comment: Applied Mathematics and Optimization, 201
Logarithmic asymptotics of the densities of SPDEs driven by spatially correlated noise
We consider the family of stochastic partial differential equations indexed
by a parameter \eps\in(0,1], \begin{equation*} Lu^{\eps}(t,x) =
\eps\sigma(u^\eps(t,x))\dot{F}(t,x)+b(u^\eps(t,x)), \end{equation*}
(t,x)\in(0,T]\times\Rd with suitable initial conditions. In this equation,
is a second-order partial differential operator with constant coefficients,
and are smooth functions and is a Gaussian noise, white
in time and with a stationary correlation in space. Let p^\eps_{t,x} denote
the density of the law of u^\eps(t,x) at a fixed point
(t,x)\in(0,T]\times\Rd. We study the existence of \lim_{\eps\downarrow 0}
\eps^2\log p^\eps_{t,x}(y) for a fixed . The results apply to a class
of stochastic wave equations with and to a class of stochastic
heat equations with .Comment: 39 pages. Will be published in the book " Stochastic Analysis and
Applications 2014. A volume in honour of Terry Lyons". Springer Verla
Using the Schramm-Loewner evolution to explain certain non-local observables in the 2d critical Ising model
We present a mathematical proof of theoretical predictions made by Arguin and
Saint-Aubin, as well as by Bauer, Bernard, and Kytola, about certain non-local
observables for the two-dimensional Ising model at criticality by combining
Smirnov's recent proof of the fact that the scaling limit of critical Ising
interfaces can be described by chordal SLE(3) with Kozdron and Lawler's
configurational measure on mutually avoiding chordal SLE paths. As an extension
of this result, we also compute the probability that an SLE(k) path, k in
(0,4], and a Brownian motion excursion do not intersect.Comment: v1: 17 pages, 4 figures, to appear in J. Phys. A: Math. Theor
Heart-lung-muscle anti-SAE syndrome : an atypical severe combination
A 78-year-old man with 3 months of progressive dyspnea, dysphony, dysgeusia, and proximal muscle weakness was diagnosed of probably idiopathic inflammatory myopathy with nonspecific interstitial pneumonia. Variable degrees of atrioventricular block and persistently elevated cardiac enzymes indicated a diagnosis of myocarditis, confirmed with cardiac magnetic resonance imaging and endomyocardial biopsy. A comprehensive immune work-up revealed anti-small ubiquitin-like modifier-1 activating enzyme (anti-SAE) antibody, a novel myositis-specific antibody, previously described mainly with overt cutaneous dermatomyositis and late skeletal muscle manifestations. Here, heart-lung-muscle involvement combined with anti-SAE antibodies was a severe combination
The physics of spreading processes in multilayer networks
The study of networks plays a crucial role in investigating the structure,
dynamics, and function of a wide variety of complex systems in myriad
disciplines. Despite the success of traditional network analysis, standard
networks provide a limited representation of complex systems, which often
include different types of relationships (i.e., "multiplexity") among their
constituent components and/or multiple interacting subsystems. Such structural
complexity has a significant effect on both dynamics and function. Throwing
away or aggregating available structural information can generate misleading
results and be a major obstacle towards attempts to understand complex systems.
The recent "multilayer" approach for modeling networked systems explicitly
allows the incorporation of multiplexity and other features of realistic
systems. On one hand, it allows one to couple different structural
relationships by encoding them in a convenient mathematical object. On the
other hand, it also allows one to couple different dynamical processes on top
of such interconnected structures. The resulting framework plays a crucial role
in helping achieve a thorough, accurate understanding of complex systems. The
study of multilayer networks has also revealed new physical phenomena that
remain hidden when using ordinary graphs, the traditional network
representation. Here we survey progress towards attaining a deeper
understanding of spreading processes on multilayer networks, and we highlight
some of the physical phenomena related to spreading processes that emerge from
multilayer structure.Comment: 25 pages, 4 figure
Despertar la curiosidad por la química desde la Universidad
En este trabajo se presentará la experiencia realizada a partir de la visita a la exposición “¿Dónde está la química?”, por parte de estudiantes de secundaria, ciclos formativos y bachillerato. Esta exposición se ha programado desde la Escola Universitària Politècnica de Manresa de la Universitat Politècnica de Catalunya, con el objetivo de acercar a los estudiantes de este nivel al conocimiento y, más que nada, a la curiosidad por el mundo de la química. Se expondrá en primer lugar el material que se presenta en la exposición, así como los resultados obtenidos en una encuesta realizada a los asistentes una vez concluida la visita, y en segundo lugar se presentarán las conclusiones obtenidas de la valoración indicada.Peer ReviewedPostprint (published version
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