 document

Kraaij, R.C. (author)We extend the BarlesPerthame procedure [4] (see also [22]) of semirelaxed limits of viscosity solutions of HamiltonJacobi equations of the type f−λHf=h to the context of noncompact spaces. The convergence result allows for equations on a ‘converging sequence of spaces’ as well as Hamiltonequations written in terms of two equations in...journal article 2022
 document

Kraaij, R.C. (author), Redig, F.H.J. (author), VAN ZUIJLEN, WILLEM B. (author)We study the loss, recovery, and preservation of differentiability of timedependent large deviation rate functions. This study is motivated by meanfield GibbsnonGibbs transitions. The gradient of the ratefunction evolves according to a Hamiltonian flow. This Hamiltonian flow is used to analyze the regularity of the timedependent rate...journal article 2021
 document

Kraaij, R.C. (author)We establish uniqueness for a class of firstorder HamiltonJacobi 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
 document

Kraaij, R.C. (author), Schlottke, Mikola C. (author)We study the wellposedness 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
 document

Kraaij, R.C. (author)We study the HamiltonJacobi equation f − λHf = h, where Hf = e<sup>−f</sup> Ae<sup>f</sup> and where A is an operator that corresponds to a wellposed martingale problem. We identify an operator that gives viscosity solutions to the HamiltonJacobi equation, and which can therefore be interpreted as the resolvent of H. The operator is given...journal article 2020
 document

Collet, F. (author), Gorny, Matthias (author), Kraaij, R.C. (author)The dynamical CurieWeiss model of selforganized criticality (SOC) was introduced in (Ann. Inst. Henri Poincaré Probab. Stat. 53 (2017) 658678) and it is derived from the classical generalized CurieWeiss by imposing a microscopic Markovian evolution having the distribution of the CurieWeiss model of SOC (Ann. Probab. 44 (2016) 444478) as...journal article 2020
 document

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 largedeviation limits. We demonstrate how the GENERIC structure naturally arises from a certain symmetry in the Hamiltonian, which extends earlier work that has connected the largedeviation...journal article 2020
 document

Collet, F. (author), Kraaij, R.C. (author)We modify the spinflip dynamics of the Curie–Weiss model with dissipation in Dai Pra, Fischer and Regoli (2013) by considering arbitrary transition rates and we analyze the phaseportrait as well as the dynamics of moderate fluctuations for macroscopic observables. We obtain pathspace moderate deviation principles via a general analytic...journal article 2020
 document

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 wellposedness of a...journal article 2020
 document

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
 document

Collet, F. (author), Kraaij, R.C. (author)We analyze the dynamics of moderate fluctuations for macroscopic observables of the random field CurieWeiss model (i.e., standard CurieWeiss model embedded in a sitedependent, i.i.d. random environment). We obtain pathspace moderate deviation principles via a general analytic approach based on convergence of nonlinear generators and...journal article 2018
 document

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
 document
 Kraaij, R.C. (author) doctoral thesis 2016
 document

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 τadditive Borel measures as a continuous dual space. We prove a BanachDieudonné type result for the space of bounded continuous functions equipped with β: the finest locally convex topology on the dual...journal article 2016
 document

Kraaij, R.C. (author)We prove the large deviation principle (LDP) for the trajectory of a broad class of finite state meanfield 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
 document

Kraaij, R.C. (author)We consider locally equicontinuous strongly continuous semigroups on locally convex spaces (X,?) that are also equipped with a ‘suitable’ auxiliary norm. We introduce the set N of ? continuous seminorms 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