1,721,063 research outputs found
On Some Stochastic Hyperbolic Equations with Symplectic Characteristics
Full text linkWe study the effect of Gaussian perturbations on a class of model hyperbolic partial differential equations with double symplectic characteristics in low spatial dimensions. The coefficients of our partial differential operators contain harmonic oscillators in the space variables, while the noise is additive, white in time and colored in space. We provide sufficient conditions on the spectral measure of the covariance functional describing the noise that allows for the existence of a random field solution for the resulting stochastic partial differential equation. Furthermore, we show how the symplectic structure of the set of multiple points affects the regularity of the noise needed to build a measurable process solution. Our approach is based on some explicit computations for the fundamental solutions of several model partial differential operators together with their explicit Fourier transforms
A copula-based hierarchical hybrid loss distribution
Full text linkWe propose a model for the computation of the loss probability distribution allowing to take into
account the not-exchangeable behavior of a portfolio clustered into several classes of homogeneous loans.
These classes are classied as ‘large’ or ‘small’ depending on their cardinality. The hierarchical hybrid copulabased
model (HHC for short) follows the idea of the clusterized homogeneous copula-based approach (CHC)
and its limiting version or the limiting clusterized copula-based model (LCC) proposed in our earlier work.
This model allows us to recover a possible risk hierarchy. We suggest an algorithm to compute the HHC loss
distribution andwe compare this cdf with that computed through the CHC and LCC approaches (in the Gaussian
and Archimedean limit) and also with the pure limiting approaches which are commonly used for highdimensional
problems. We study the scalability of the algorithm
Multi-objective optimization of the inter-story isolation system used as a structural TMD
No full textInter-story isolation system (IIS) is increasingly being sought to add floors on top of existing buildings while controlling their base shear forces. One of the main issues with this application is the need to control the drift between the two structural parts and the acceleration of the superstructure, while optimizing the substructure performance. Therefore, this study investigates the use of the IIS as a structural Tuned Mass Damper (TMD), proposing a specific multi-objective optimization approach and providing new design equations for the IIS parameters. Unlike conventional TMD approaches, which focus on the performance of the primary structure (i.e., substructure), the proposed approach aims to consider the overall structural response. The optimal solutions obtained are then compared with the consistent ones currently available in the literature. Finally, time-history analyses of three simple case study structures are performed to validate these optimized solutions. The results demonstrate the potential of the IIS in improving the seismic performance of the substructure, as well as the possibility of limiting the isolation drifts and superstructure accelerations according to specific needs
Distorted Copula-Based Probability Distribution of a Counting Hierarchical Variable: A Credit Risk Application
No full textIn this paper, we propose a novel approach for the computation of the probability distribution of
a counting variable linked to a multivariate hierarchical Archimedean copula function. The
hierarchy has a twofold impact: it acts on the aggregation step but also it determines the arrival
policy of the random event. The novelty of this work is to introduce this policy, formalized as an
arrival matrix, i.e., a random matrix of dependent 0–1 random variables, into the model. This
arrival matrix represents the set of distorted (by the policy itself) combinatorial distributions of
the event, i.e., of the most probable scenarios. To this distorted version of the CHC approach [see
Ref. 7 and Ref. 27], we are now able to apply a pure hierarchical Archimedean dependence
structure among variables. As an empirical application, we study the problem of evaluating the
probability distribution of losses related to the default of various type of counterparts in a
structured portfolio exposed to the credit risk of a selected set among the major banks of European
area and to the correlations among these risks
Cauchy problem for effectively hyperbolic operators with triple characteristics of variable multiplicity
Full text linkWe study a class of third-order hyperbolic operators P in G = {(t, x): 0 ≤ t ≤ T, x ∈ U ⋐ Rn} with triple characteristics at ρ = (0, x0, ξ), ξ ∈ Rn ∖{0}. We consider the case when the fundamental matrix of the principal symbol of P at ρ has a couple of non-vanishing real eigenvalues. Such operators are called effectively hyperbolic. Ivrii introduced the conjecture that every effectively hyperbolic operator is strongly hyperbolic, that is the Cauchy problem for P + Q is locally well posed for any lower order terms Q. This conjecture has been solved for operators having at most double characteristics and for operators with triple characteristics in the case when the principal symbol admits a factorization. A strongly hyperbolic operator in G could have triple characteristics in G only for t = 0 or for t = T. We prove that the operators in our class are strongly hyperbolic if T is small enough. Our proof is based on energy estimates with a loss of regularity
Evaluation of optimal FVDs for inter-storey isolation systems based on surrogate performance models
Full text linkInter-storey seismic isolation is increasingly gaining attention. One of the main related issues is the need to limit the relative displacement between substructure and superstructure, while maintaining a good seismic performance of the superstructure. As shown in some studies, fluid viscous dampers (FVDs) mounted in isolation systems are effective in reducing isolator deflection but can be harmful by amplifying inter-storey drifts and floor accelerations. Additionally, the effectiveness of FVDs for inter-storey applications was investigated only recently, and specific approaches for their optimisation and performance evaluation are missing. Therefore, this paper proposes a method for the optimal multi-objective design of FVDs, based on the definition of appropriate surrogate response models, which allows for rationally comparing the FVD effects for a wide range of dampers and structures. In particular, the optimal FVD parameters are provided in a dimensionless form, so that they can be predicted by design equations of general validity within the range of the structures analysed. This method is applied to a stock of regular structures with various vibration periods of superstructure, isolation and substructure, examining a linear and a non-linear isolation system and a set of natural records, in order to comprehensively assess the effects of FVDs and their non-linearity on the seismic performance of these structures. Finally, prediction models of optimal FVD parameters are provided based on the results obtained and are applied to three case studies as an example
Tracking Time Varying Parameters Via Online Simplified Maximum Likelihood
Full text linkUsually, log-likelihood functions fail to satisfy the classical assumptions of strong
convexity and Lipschitz-continuity of the gradient (as well as many of their mild
counterparts) that are common in general convergence results for stochastic gradi-
ent descent algorithms. Therefore, the use of gradient descent schemes to track the
maxima of a sequence of objective log-likelihood functions suffers from the lack of
theoretical results that guarantee the validity of the method. In this paper, we propose
a simplified online scheme to track unknown dynamic parameters that are the optima
of a sequence of objective log-likelihood functions. Under a Lipschitz assumption on
the time varying optimum we demonstrate that our estimator achieves mean square
convergence up to a neighborhood of the optimum, and we establish that the Lipschitz
continuity assumption is necessary when a specific desirable property is imposed.
The method is inspired by a Taylor expansion of the log-likelihood function around
the maximum likelihood estimator, and rigorously justified by the expression for the
Riemannian gradient of the log-likelihood of a multivariate Gaussian distribution
COUNTEREXAMPLES TO C ∞ WELL POSEDNESS FOR SOME HYPERBOLIC OPERATORS WITH TRIPLE CHARACTERISTICS
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