Searched for: subject%3A%22Hamilton%255CJacobi%255C%2Bequation%22
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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
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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 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
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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
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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
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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
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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
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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 wellposedness 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 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
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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)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
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Melikyan, A. (author), Olsder, G.J. (author)Boundaryvalue problems for first order PDEs are locally considered, when the classical sufficient condition for the solution existence does not hold, but a solution still exists, possibly defined on one or both sides of the boundary surface. We note three situations when such a surface (locally) arises: (1) the part of the boundary surface with...journal article 2010
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