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Scaling precipitation extremes with temperature in the Mediterranean: past climate assessment and projection in anthropogenic scenarios
No full textInternational audienceIn this study we investigate the scaling of precipitation extremes with temperature in the Mediterranean region by assessing against observations the present day and future regional climate simulations performed in the frame of the HyMeX and MED-CORDEX programs. Over the 1979–2008 period, despite differences in quantitative precipitation simulation across the various models, the change in precipitation extremes with respect to temperature is robust and consistent. The spatial variability of the temperature–precipitation extremes relationship displays a hook shape across the Mediterranean, with negative slope at high temperatures and a slope following Clausius–Clapeyron (CC)-scaling at low temperatures. The temperature at which the slope of the temperature–precipitation extreme relation sharply changes (or temperature break), ranges from about 20 °C in the western Mediterranean to <10 °C in Greece. In addition, this slope is always negative in the arid regions of the Mediterranean. The scaling of the simulated precipitation extremes is insensitive to ocean–atmosphere coupling, while it depends very weakly on the resolution at high temperatures for short precipitation accumulation times. In future climate scenario simulations covering the 2070–2100 period, the temperature break shifts to higher temperatures by a value which is on average the mean regional temperature change due to global warming. The slope of the simulated future temperature–precipitation extremes relationship is close to CC-scaling at temperatures below the temperature break, while at high temperatures, the negative slope is close, but somewhat flatter or steeper, than in the current climate depending on the model. Overall, models predict more intense precipitation extremes in the future. Adjusting the temperature–precipitation extremes relationship in the present climate using the CC law and the temperature shift in the future allows the recovery of the temperature–precipitation extremes relationship in the future climate. This implies negligible regional changes of relative humidity in the future despite the large warming and drying over the Mediterranean. This suggests that the Mediterranean Sea is the primary source of moisture which counteracts the drying and warming impacts on relative humidity in parts of the Mediterranean region
Convergence of discrete-time Kalman filter estimate to continuous-time estimate for systems with unbounded observation
No full textThis is the preprint version of the article published in Mathematics of Control, Signals and SystemsInternational audienceIn this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal discretization is refined, the estimate converges to the continuous-time estimate given by the Kalman–Bucy filter. We shall give bounds for the convergence rates for the variance of the discrepancy between these two estimates. The contribution of this article is to generalize the convergence results to systems with unbounded observation operators under different sets of assumptions, including systems with diagonaliz-able generators, systems with admissible observation operators, and systems with analytic semigroups. The proofs are based on applying the discrete-time Kalman filter on a dense, numerable subset on the time interval [0,T] and bounding the increments obtained. These bounds are obtained by studying the regularity of the underlying semigroup and the noise-free output
Quadratic backward stochastic differential equations driven by -Brownian motion: discrete solutions and approximation
No full textInternational audienceIn this paper, we consider backward stochastic differential equations driven by -Brownian motion (GBSDEs) under quadratic assumptions on coefficients. We prove the existence and uniqueness of solution for such equations. On the one hand, a priori estimates are obtained by applying the Girsanov type theorem in the -framework, from which we deduce the uniqueness. On the other hand, to prove the existence of solutions, we first construct solutions for discrete GBSDEs by solving corresponding fully nonlinear PDEs, and then approximate solutions for general quadratic GBSDEs in Banach spaces
Efficient Bayesian Computation by Proximal Markov Chain Monte Carlo: When Langevin Meets Moreau.
No full textInternational audienceIn this paper, two new algorithms to sample from possibly non-smooth log-concave probability measures are introduced. These algorithms use Moreau-Yosida envelope combined with the Euler-Maruyama discretization of Langevin diffusions. They are applied to a de-convolution problem in image processing, which shows that they can be practically used in a high dimensional setting. Finally, non-asymptotic bounds for one of the proposed methods are derived. These bounds follow from non-asymptotic results for ULA applied to probability measures with a convex continuously differentiable log-density with respect to the Lebesgue measure
Regularity of BSDEs with a convex constraint on the gains-process
No full textWe consider the minimal super-solution of a backward stochastic differential equation with constraint on the gains-process. The terminal condition is given by a function of the terminal value of a forward stochastic differential equation. Under boundedness assumptions on the coefficients, we show that the first component of the solution is Lipschitz in space and 1/2-Hölder in time with respect to the initial data of the forward process. Its path is continuous before the time horizon at which its left-limit is given by a face-lifted version of its natural boundary condition. This first component is actually equal to its own face-lift. We only use probabilistic arguments. In particular, our results can be extended to certain non-Markovian settings
A unified approach to a priori estimates for supersolutions of BSDEs in general filtrations
No full textInternational audienceWe provide a unified approach to a priori estimates for supersolutions of BSDEs in general filtrations, which may not be quasi left-continuous. As an example of application, we prove that reflected BSDEs are well-posed in a general framework.Nous proposons dans cet article une approche unifiée permettant l’obtention d’estimées a priori pour des sur-solutions d’EDSR adaptées à des filtrations générales, en particulier non nécessairement quasi-continues à gauche. Contrairement aux approches antérieures de ce problème dans des cadres plus simples, nos résultats ne sont pas la conséquence directe de la formule d’Itô et d’estimées classiques, mais dépendent de manière cruciale de versions appropriées à notre contexte d’estimées obtenues par Meyer pour des sur-martingales. Nous proposons entre autres une application de nos résultats à l’étude de l’existence et de l’unicité de solutions d’EDSR réfléchies dans un cadre général non-couvert par les résultats précédents dans la littérature
Null-controllability of hypoelliptic quadratic differential equations
No full text46 pagesInternational audienceWe study the null-controllability of parabolic equations associated to a general class of hypoelliptic quadratic differential operators. Quadratic differential operators are operators defined in the Weyl quantization by complex-valued quadratic symbols. We consider in this work the class of accretive quadratic operators with zero singular spaces. These possibly degenerate non-selfadjoint differential operators are known to be hypoelliptic and to generate contraction semigroups which are smoothing in specific Gelfand-Shilov spaces for any positive time. Thanks to this regularizing effect, we prove by adapting the Lebeau-Robbiano method that parabolic equations associated to these operators are null-controllable in any positive time from control regions, for which null-controllability is classically known to hold in the case of the heat equation on the whole space. Some applications of this result are then given to the study of parabolic equations associated to hypoelliptic Ornstein-Uhlenbeck operators acting on weighted spaces with respect to invariant measures. By using the same strategy, we also establish the null-controllability in any positive time from the same control regions for parabolic equations associated to any hypoelliptic Ornstein-Uhlenbeck operator acting on the flat space extending in particular the known results for the heat equation or the Kolmogorov equation on the whole space
Characterization of vertical cloud variability over Europe using spatial lidar observations and regional simulation
No full textInternational audienceIn this paper we characterize the seasonal and inter-annual variabilities of cloud fraction profiles in both observations and simulation since they are critical to better assess the impact of clouds on climate variability. The spaceborne lidar onboard CALIPSO, providing cloud vertical profiles since 2006, is used together with a 23-year WRF simulation at 20 km resolution. A lidar simulator helps to compare consistently model with observations. The bias in observations due to the satellite under-sampling is first estimated. Then we examine the vertical variability of both occurrence and properties of clouds. It results that observations indicate a similar occurrence of low and high clouds over continent, and more high than low clouds over the sea except in summer. The simulation shows an overestimate (underestimate) of high (low) clouds comparing to observations, especially in summer. However the seasonal variability of cloud vertical profiles is well captured by WRF. Concerning inter-annual variability, observations show that in winter, those of high clouds is twice the low clouds one, an order of magnitude that is is well simulated. In summer, the observed inter-annual variability is vertically more homogeneous while the model still simulates more variability for high clouds than for low clouds. The good behavior of the simulation in winter allows us to use the 23 years of simulation and 8 years of observations to estimate the time period required to characterize the natural variability of the cloud fraction profile in winter, i.e. the time period required to detect significant anomalies and trends
Analytical approximations of local-Heston volatility model and error analysis
No full textInternational audienceThis paper consists in providing and mathematically analyzing the expansion of an option price (with bounded Lipschitz payoff) for model combining local and stochastic volatility. The local volatility part has a general form, with appropriate growth and boundedness assumptions. For the stochastic part, we choose a square root process, which is widely used for modeling the behavior of the variance process (Heston model). We rigorously establish tight error estimates of our expansions, using Malliavin calculus, which requires a careful treatment because of the lack of weak differentiability of the model; this error analysis is interesting on its own. Moreover, in the particular case of Call-Put options, we also provide expansions of the Black-Scholes implied volatility which allows to obtain very simple and rapid formulas in comparison to the Monte Carlo approach while maintaining a very competitive accuracy
Classification of Special Curves in the Space of Cubic Polynomials
No full textInternational audienceWe describe all special curves in the parameter space of complex cubic polynomials, that is all algebraic irreducible curves containing infinitely many post-critically finite polynomials. This solves in a strong form a conjecture by Baker and DeMarco for cubic polynomials. We also prove that an irreducible component of the algebraic curve consisting of those cubic polynomials that admit an orbit of any given period and multiplier is special if and only if the multiplier is 0