Articles (Departament d'Economia)
http://hdl.handle.net/10230/8584
2021-02-28T14:05:57ZYears of life lost to COVID-19 in 81 countries
http://hdl.handle.net/10230/46573
Years of life lost to COVID-19 in 81 countries
Pifarré Arolas, Hèctor; Acosta, Enrique; López i Casasnovas, Guillem; Lo, Adeline; Nicodemo, Catia; Riffe, Tim; Myrskylä, Mikko
Understanding the mortality impact of COVID-19 requires not only counting the dead, but analyzing how premature the deaths are. We calculate years of life lost (YLL) across 81 countries due to COVID-19 attributable deaths, and also conduct an analysis based on estimated excess deaths. We find that over 20.5 million years of life have been lost to COVID-19 globally. As of January 6, 2021, YLL in heavily affected countries are 2–9 times the average seasonal influenza; three quarters of the YLL result from deaths in ages below 75 and almost a third from deaths below 55; and men have lost 45% more life years than women. The results confirm the large mortality impact of COVID-19 among the elderly. They also call for heightened awareness in devising policies that protect vulnerable demographics losing the largest number of life-years.
2021-01-01T00:00:00ZA local-time correspondence for stochastic partial differential equations
http://hdl.handle.net/10230/46563
A local-time correspondence for stochastic partial differential equations
Foondun, Mohammud; Khoshnevisan, Davar; Nualart, Eulàlia
It is frequently the case that a white-noise-driven parabolic and/or hyperbolic stochastic partial differential equation (SPDE) can have random-field solutions only in spatial dimension one. Here we show that in many cases, where the ``spatial operator'' is the $ L^2$-generator of a Lévy process $ X$, a linear SPDE has a random-field solution if and only if the symmetrization of $ X$ possesses local times. This result gives a probabilistic reason for the lack of existence of random-field solutions in dimensions strictly larger than one.
In addition, we prove that the solution to the SPDE is [Hölder] continuous in its spatial variable if and only if the said local time is [Hölder] continuous in its spatial variable. We also produce examples where the random-field solution exists, but is almost surely unbounded in every open subset of space-time. Our results are based on first establishing a quasi-isometry between the linear $ L^2$-space of the weak solutions of a family of linear SPDEs, on one hand, and the Dirichlet space generated by the symmetrization of $ X$, on the other hand.
We mainly study linear equations in order to present the local-time correspondence at a modest technical level. However, some of our work has consequences for nonlinear SPDEs as well. We demonstrate this assertion by studying a family of parabolic SPDEs that have additive nonlinearities. For those equations we prove that if the linearized problem has a random-field solution, then so does the nonlinear SPDE. Moreover, the solution to the linearized equation is [Hölder] continuous if and only if the solution to the nonlinear equation is, and the solutions are bounded and unbounded together as well. Finally, we prove that in the cases where the solutions are unbounded, they almost surely blow up at exactly the same points.
2011-01-01T00:00:00ZOn the density of systems of non-linear spatially homogeneous SPDEs
http://hdl.handle.net/10230/46562
On the density of systems of non-linear spatially homogeneous SPDEs
Nualart, Eulàlia
In this paper, we consider a system of k second-order nonlinear stochastic partial differential equations with spatial dimension , driven by a q-dimensional Gaussian noise, which is white in time and with some spatially homogeneous covariance. The case of a single equation and a one-dimensional noise has largely been studied in the literature. The first aim of this paper is to give a survey of some of the existing results. We will start with the existence, uniqueness and Hölder's continuity of the solution. For this, the extension of Walsh's stochastic integral to cover some measure-valued integrands will be recalled. We will then recall the results concerning the existence and smoothness of the density, as well as its strict positivity, which are obtained using techniques of Malliavin calculus. The second aim of this paper is to show how these results extend to our system of stochastic partial differential equations (SPDEs). In particular, we give sufficient conditions in order to have existence and smoothness of the density on the set where the columns of the diffusion matrix span . We then prove that the density is strictly positive in a point if the connected component of the set where the columns of the diffusion matrix span which contains this point has a non-void intersection with the support of the law of the solution. We will finally check how all these results apply to the case of the stochastic heat equation in any space dimension and the stochastic wave equation in dimension.
2012-01-01T00:00:00ZExistence and regularity of the density for solutions to semilinear dissipative parabolic SPDEs
http://hdl.handle.net/10230/46561
Existence and regularity of the density for solutions to semilinear dissipative parabolic SPDEs
Marinelli, Carlo; Nualart, Eulàlia; Quer-Sardanyons, Lluís
We prove existence and smoothness of the density of the solution to a nonlinear stochastic heat equation on L2(O) (evaluated at fixed points in time and space), where O is an open bounded domain in ℝd with smooth boundary. The equation is driven by an additive Wiener noise and the nonlinear drift term is the superposition operator associated to a real function which is assumed to be (maximal) monotone, continuously differentiable, and growing not faster than a polynomial. The proof uses tools of the Malliavin calculus combined with methods coming from the theory of maximal monotone operators.
2013-01-01T00:00:00Z