| 1. |
- Abatangelo, Laura, et al.
(författare)
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Eigenvalue variation under moving mixed Dirichlet–Neumann boundary conditions and applications
- 2020
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Ingår i: ESAIM. - : EDP Sciences. - 1292-8119 .- 1262-3377. ; 26
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Tidskriftsartikel (refereegranskat)abstract
- We deal with the sharp asymptotic behaviour of eigenvalues of elliptic operators with varying mixed Dirichlet–Neumann boundary conditions. In case of simple eigenvalues, we compute explicitly the constant appearing in front of the expansion’s leading term. This allows inferring some remarkable consequences for Aharonov–Bohm eigenvalues when the singular part of the operator has two coalescing poles.
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| 2. |
- Escobar, Jesica, et al.
(författare)
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INSTRUMENTAL VARIABLES AND LSM IN CONTINUOUS-TIME PARAMETER ESTIMATION
- 2017
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Ingår i: ESAIM. - : EDP SCIENCES S A. - 1292-8119 .- 1262-3377. ; 23:2, s. 427-442
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Tidskriftsartikel (refereegranskat)abstract
- In this paper the main goal is to compare the instrumental variables and the least squares methods applied to parameter estimation in continuous-time systems, avoiding any preliminary discretization of the process, and to analyse which method is more suitable for estimation in continuous-time under stochastic perturbations. A numerical example illustrates the effectiveness of the algorithms.
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| 3. |
- Makhlouf, K., et al.
(författare)
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SPDEs with space interactions and application to population modelling
- 2023
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Ingår i: ESAIM. - : EDP Sciences. - 1292-8119 .- 1262-3377. ; 29
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Tidskriftsartikel (refereegranskat)abstract
- We consider optimal control of a new type of non-local stochastic partial differential equations (SPDEs). The SPDEs have space interactions, in the sense that the dynamics of the system at time t and position in space x also depend on the space-mean of values at neighbouring points. This is a model with many applications, e.g. to population growth studies and epidemiology. We prove the existence and uniqueness of strong, smooth solutions of a class of SPDEs with space interactions, and we show that, under some conditions, the solutions are positive for all times if the initial values are. Sufficient and necessary maximum principles for the optimal control of such systems are derived. Finally, we apply the results to study an optimal vaccine strategy problem for an epidemic by modelling the population density as a space-mean stochastic reaction-diffusion equation.
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| 4. |
- Perninge, Magnus, 1980-
(författare)
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Probabilistic representation of viscosity solutions to quasi-variational inequalities with non-local drivers
- 2023
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Ingår i: ESAIM. - : EDP Sciences. - 1292-8119 .- 1262-3377. ; 29
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Tidskriftsartikel (refereegranskat)abstract
- We consider quasi-variational inequalities (QVIs) with general non-local drivers and related systems of reflected backward stochastic differential equations (BSDEs) in a Brownian filtration. We show existence and uniqueness of viscosity solutions to the QVIs by first considering the standard (local) setting and then applying a contraction argument. In addition, the contraction argument yields existence and uniqueness of solutions to the related systems of reflected BSDEs and extends the theory of probabilistic representations of PDEs in terms of BSDEs to our specific setting.
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