Searched for: author%3A%22Kraaij%2C+R.C.%22
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Kraaij, R.C. (author)
We extend the Barles-Perthame procedure [4] (see also [22]) of semi-relaxed limits of viscosity solutions of Hamilton-Jacobi equations of the type f−λHf=h to the context of non-compact spaces. The convergence result allows for equations on a ‘converging sequence of spaces’ as well as Hamilton-equations written in terms of two equations in...
journal article 2022
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Kraaij, R.C. (author), Redig, F.H.J. (author), VAN ZUIJLEN, WILLEM B. (author)
We study the loss, recovery, and preservation of differentiability of time-dependent large deviation rate functions. This study is motivated by mean-field Gibbs-non-Gibbs transitions. The gradient of the rate-function evolves according to a Hamiltonian flow. This Hamiltonian flow is used to analyze the regularity of the time-dependent rate...
journal article 2021
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Kraaij, R.C. (author)
We establish uniqueness for a class of first-order Hamilton-Jacobi equations with Hamiltonians that arise from the large deviations of the empirical measure and empirical flux pair of weakly interacting Markov jump processes. As a corollary, we obtain such a large deviation principle in the context of weakly interacting processes with time...
journal article 2021
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Kraaij, R.C. (author), Schlottke, Mikola C. (author)
We study the well-posedness of Hamilton–Jacobi–Bellman equations on subsets of R<sup>d</sup> in a context without boundary conditions. The Hamiltonian is given as the supremum over two parts: an internal Hamiltonian depending on an external control variable and a cost functional penalizing the control. The key feature in this paper is that...
journal article 2021
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Kraaij, R.C. (author)
We study the Hamilton-Jacobi equation f − λHf = h, where Hf = e<sup>−f</sup> Ae<sup>f</sup> and where A is an operator that corresponds to a well-posed martingale problem. We identify an operator that gives viscosity solutions to the Hamilton-Jacobi equa-tion, and which can therefore be interpreted as the resolvent of H. The operator is given...
journal article 2020
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Collet, F. (author), Gorny, Matthias (author), Kraaij, R.C. (author)
The dynamical Curie-Weiss model of self-organized criticality (SOC) was introduced in (Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 658-678) and it is derived from the classical generalized Curie-Weiss by imposing a microscopic Markovian evolution having the distribution of the Curie-Weiss model of SOC (Ann. Probab. 44 (2016) 444-478) as...
journal article 2020
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Kraaij, R.C. (author), Lazarescu, Alexandre (author), Maes, Christian (author), Peletier, Mark (author)
We develop a formalism to discuss the properties of GENERIC systems in terms of corresponding Hamiltonians that appear in the characterization of large-deviation limits. We demonstrate how the GENERIC structure naturally arises from a certain symmetry in the Hamiltonian, which extends earlier work that has connected the large-deviation...
journal article 2020
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Collet, F. (author), Kraaij, R.C. (author)
We modify the spin-flip dynamics of the Curie–Weiss model with dissipation in Dai Pra, Fischer and Regoli (2013) by considering arbitrary transition rates and we analyze the phase-portrait as well as the dynamics of moderate fluctuations for macroscopic observables. We obtain path-space moderate deviation principles via a general analytic...
journal article 2020
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Kraaij, R.C. (author), Mahé, Louis (author)
We prove Freidlin–Wentzell type large deviation principles for various rescaled models in populations dynamics that have immigration and possibly harvesting: birth–death processes, Galton–Watson trees, epidemic SI models, and prey–predator models. The proofs are carried out using a general analytic approach based on the well-posedness of a...
journal article 2020
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Kraaij, R.C. (author), Redig, F.H.J. (author), Versendaal, R. (author)
We generalize classical large deviation theorems to the setting of complete, smooth Riemannian manifolds. We prove the analogue of Mogulskii's theorem for geodesic random walks via a general approach using viscosity solutions for Hamilton–Jacobi equations. As a corollary, we also obtain the analogue of Cramér's theorem. The approach also...
journal article 2019
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Collet, F. (author), Kraaij, R.C. (author)
We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field Curie-Weiss model (i.e., standard Curie-Weiss model embedded in a site-dependent, i.i.d. random environment). We obtain path-space moderate deviation principles via a general analytic approach based on convergence of nonlinear generators and...
journal article 2018
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Collet, F. (author), Kraaij, R.C. (author)
We derive moderate deviation principles for the trajectory of the empirical magnetization of the standard Curie–Weiss model via a general analytic approach based on convergence of generators and uniqueness of viscosity solutions for associated Hamilton–Jacobi equations. The moderate asymptotics depend crucially on the phase under consideration.
journal article 2017
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Kraaij, R.C. (author)
doctoral thesis 2016
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Kraaij, R.C. (author)
Let X be a separable metric space and let β be the strict topology on the space of bounded continuous functions on X, which has the space of τ-additive Borel measures as a continuous dual space. We prove a Banach-Dieudonné type result for the space of bounded continuous functions equipped with β: the finest locally convex topology on the dual...
journal article 2016
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Kraaij, R.C. (author)
We prove the large deviation principle (LDP) for the trajectory of a broad class of finite state mean-field interacting Markov jump processes via a general analytic approach based on viscosity solutions. Examples include generalized Ehrenfest models as well as Curie–Weiss spin flip dynamics with singular jump rates. The main step in the proof of...
journal article 2016
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Kraaij, R.C. (author)
We consider locally equi-continuous strongly continuous semigroups on locally convex spaces (X,?) that are also equipped with a ‘suitable’ auxiliary norm. We introduce the set N of ? -continuous semi-norms that are bounded by the norm. If (X,?) has the property that N is closed under countable convex combinations, then a number of Banach space...
journal article 2015
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