| 51. |
- Thörnblad, Karin, 1971, et al.
(författare)
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Scheduling optimization of a real flexible job shop including side constraints regarding maintenance, fixtures, and night shifts
- 2013
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We present a generic iterative scheduling procedure for the scheduling of a real flexible job shop, the so-called multitask cell at GKN Aerospace Engine Systems in Sweden. A time-indexed formulation of the problem is presented including side constraints regarding preventive maintenance, fixture availability, and unmanned night shifts. This paper continues the work in [35], with an improvement of the iterative solution procedure and the inclusion of constraints regarding night shifts during which only unmanned processing is allowed. The resulting schedules are compared with schedules constructed using two priority dispatching rules. Computational results show that the gain of including the night shifts constraints is significant and that the methodology developed is able to produce near-optimal schedules for industrial data instances for the coming shift within an acceptable practical time frame.
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| 52. |
- Beilina, Larisa, 1970, et al.
(författare)
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Lipschitz stability for an inverse hyperbolic problem of determining two coefficients by a finite number of observations
- 2018
-
Ingår i: Inverse Problems. - : IOP Publishing. - 0266-5611 .- 1361-6420. ; 34:1
-
Tidskriftsartikel (refereegranskat)abstract
- We consider an inverse problem of reconstructing two spatially varying coefficients in an acoustic equation of hyperbolic type using interior data of solutions with suitable choices of initial condition. Using a Carleman estimate, we prove Lipschitz stability estimates which ensure unique reconstruction of both coefficients. Our theoretical results are justified by numerical studies on the reconstruction of two unknown coefficients using noisy backscattered data.
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| 53. |
- Belomestny, Denis, et al.
(författare)
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Weak solutions to gamma-driven stochastic differential equations
- 2023
-
Ingår i: Indagationes Mathematicae. - 0019-3577. ; 34:4, s. 820-829
-
Tidskriftsartikel (refereegranskat)abstract
- We study a stochastic differential equation driven by a gamma process, for which we give results on the existence of weak solutions under conditions on the volatility function. To that end we provide results on the density process between the laws of solutions with different volatility functions.
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| 54. |
- Bolin, David, 1983, et al.
(författare)
-
Weak convergence of Galerkin approximations for fractional elliptic stochastic PDEs with spatial white noise
- 2018
-
Ingår i: BIT (Copenhagen). - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 58:4, s. 881-906
-
Tidskriftsartikel (refereegranskat)abstract
- The numerical approximation of the solution to a stochastic partial differential equation with additive spatial white noise on a bounded domain is considered. The differential operator is assumed to be a fractional power of an integer order elliptic differential operator. The solution is approximated by means of a finite element discretization in space and a quadrature approximation of an integral representation of the fractional inverse from the Dunford–Taylor calculus. For the resulting approximation, a concise analysis of the weak error is performed. Specifically, for the class of twice continuously Fréchet differentiable functionals with second derivatives of polynomial growth, an explicit rate of weak convergence is derived, and it is shown that the component of the convergence rate stemming from the stochasticity is doubled compared to the corresponding strong rate. Numerical experiments for different functionals validate the theoretical results.
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| 55. |
- Broman, Erik, 1977, et al.
(författare)
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Random cover times using the Poisson cylinder process
- 2019
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Ingår i: Alea-Latin American Journal of Probability and Mathematical Statistics. - : Institute for Applied and Pure Mathematics (IMPA). - 1980-0436. ; 16:2, s. 1165-1199
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we deal with the classical problem of random cover times. We investigate the distribution of the time it takes for a Poisson process of cylinders to cover a set A subset of R-d . This Poisson process of cylinders is invariant under rotations, reflections and translations, and in addition we add a time component so that cylinders are "raining from the sky" at unit rate. Our main results concerns the asymptotic of this cover time as the set A grows. If the set A is discrete and well separated, we show convergence of the cover time to a Gumbel distribution. If instead A has positive box dimension (and satisfies a weak additional assumption), we find the correct rate of convergence.
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| 56. |
- Bågmark, Kasper, 1995, et al.
(författare)
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An energy-based deep splitting method for the nonlinear filtering problem
- 2023
-
Ingår i: Partial Differential Equations and Applications. - : Springer Science and Business Media LLC. - 2662-2963 .- 2662-2971. ; 4:2
-
Tidskriftsartikel (refereegranskat)abstract
- The purpose of this paper is to explore the use of deep learning for the solution of the nonlinear filtering problem. This is achieved by solving the Zakai equation by a deep splitting method, previously developed for approximate solution of (stochastic) partial differential equations. This is combined with an energy-based model for the approximation of functions by a deep neural network. This results in a computationally fast filter that takes observations as input and that does not require re-training when new observations are received. The method is tested on four examples, two linear in one and twenty dimensions and two nonlinear in one dimension. The method shows promising performance when benchmarked against the Kalman filter and the bootstrap particle filter.
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| 57. |
- Casarino, V., et al.
(författare)
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On the maximal operator of a general Ornstein-Uhlenbeck semigroup
- 2022
-
Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 301
-
Tidskriftsartikel (refereegranskat)abstract
- If Q is a real, symmetric and positive definite n x n matrix, and B a real n x n matrix whose eigenvalues have negative real parts, we consider the Ornstein-Uhlenbeck semigroup on R-n with covariance Q and drift matrix B. Our main result says that the associated maximal operator is of weak type (1, 1) with respect to the invariant measure. The proof has a geometric gist and hinges on the "forbidden zones method" previously introduced by the third author.
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| 58. |
- Cleanthous, G., et al.
(författare)
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Regularity, continuity and approximation of isotropic Gaussian random fields on compact two-point homogeneous spaces
- 2020
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Ingår i: Stochastic Processes and their Applications. - : Elsevier BV. - 0304-4149. ; 130:8, s. 4873-4891
-
Tidskriftsartikel (refereegranskat)abstract
- Gaussian random fields defined over compact two-point homogeneous spaces are considered and Sobolev regularity and Hölder continuity are explored through spectral representations. It is shown how spectral properties of the covariance function associated to a given Gaussian random field are crucial to determine such regularities and geometric properties. Furthermore, fast approximations of random fields on compact two-point homogeneous spaces are derived by truncation of the series expansion, and a suitable bound for the error involved in such an approximation is provided. © 2020 Elsevier B.V.
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| 59. |
- Davydov, Michel, et al.
(författare)
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Finite thinning-selfdecomposable point processes
- 2019
-
Ingår i: Statistics and Probability Letters. - : Elsevier BV. - 0167-7152. ; 146, s. 132-138
-
Tidskriftsartikel (refereegranskat)abstract
- Thinning-selfdecomposable point processes arise as a limit in the thinning-superposition schemes of independent but not necessarily identically distributed point processes and, as such, they constitute a strict subclass of infinitely divisible point processes. At the same time they are strictly larger than the class of discrete α-stable point processes which are the limits of a scaled superposition of independent identically distributed processes. We give a series representation for finite thinning-selfdecomposable point processes which can be viewed as an analogue of an integral representation of selfdecomposable (or class L) random variables.
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| 60. |
- Eisenmann, Monika, et al.
(författare)
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Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations
- 2022
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Ingår i: Bit Numerical Mathematics. - : Springer Science and Business Media LLC. - 0006-3835 .- 1572-9125. ; 62:3, s. 803-48
-
Tidskriftsartikel (refereegranskat)abstract
- In this paper we derive error estimates of the backward Euler-Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation is a stochastic gradient flow whose associated potential is not continuously differentiable but assumed to be convex. We show that the backward Euler-Maruyama method is well-defined and convergent of order at least 1/4 with respect to the root-mean-square norm. Our error analysis relies on techniques for deterministic problems developed in Nochetto et al. (Commun Pure Appl Math 53(5):525-589, 2000). We verify that our setting applies to an overdamped Langevin equation with a discontinuous gradient and to a spatially semi-discrete approximation of the stochastic p-Laplace equation.
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