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Large deviations for Markov processes with switching and homogenisation via Hamilton–Jacobi–Bellman equations

Della Corte, S. (author), Kraaij, R.C. (author)

We consider the context of molecular motors modelled by a diffusion process driven by the gradient of a weakly periodic potential that depends on an internal degree of freedom. The switch of the internal state, that can freely be interpreted as a molecular switch, is modelled as a Markov jump process that depends on the location of the motor....

journal article 2024

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Hamilton–Jacobi equations for controlled gradient flows: The comparison principle

Conforti, G. (author), Kraaij, R.C. (author), Tonon, D. (author)

Motivated by recent developments in the fields of large deviations for interacting particle systems and mean field control, we establish a comparison principle for the Hamilton–Jacobi equation corresponding to linearly controlled gradient flows of an energy function E defined on a metric space (E,d). Our analysis is based on a systematic use...

journal article 2023

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A general convergence result for viscosity solutions of Hamilton-Jacobi equations and non-linear semigroups

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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A hamilton-jacobi point of view on mean-field gibbs-non-gibbs transitions

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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Flux large deviations of weakly interacting jump processes via well-posedness of an associated Hamilton-Jacobi equation

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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Comparison Principle for Hamilton-Jacobi-Bellman Equations via a Bootstrapping Procedure

Kraaij, R.C. (author), Schlottke, Mikola C. (author)

We study the well-posedness of Hamilton–Jacobi–Bellman equations on subsets of R^d 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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Fluctuation symmetry leads to GENERIC equations with non-quadratic dissipation

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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Well-posedness of Hamilton–Jacobi equations in population dynamics and applications to large deviations

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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Path-space moderate deviations for a Curie-Weiss model of self-organized criticality

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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The exponential resolvent of a markov process and large deviations for markov processes via hamilton-jacobi equations

Kraaij, R.C. (author)

We study the Hamilton-Jacobi equation f − λHf = h, where Hf = e^−f Ae^f 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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Path-space moderate deviations for a class of Curie–Weiss models with dissipation

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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Percutaneous interface tissue removal for hip refixation: The first step in instrument design

Kraaij, G. (author)

In the Netherlands about 36.000 total hip prostheses are implanted every year. Survival of these prostheses at 10 year follow-up is 90% in patients older than 70 years at the index operation. In younger patients these results decrease to about 80–85% at 10 years follow-up. The main cause of failure in total hip replacement is aseptic (mechanical...

doctoral thesis 2019

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Water Jet Applicator for Interface Tissue Removal in Minimally Invasive Hip Refixation: Testing the Principle and Design of Prototype

Kraaij, G. (author), Loeve, A.J. (author), Dankelman, J. (author), Nelissen, R.G.H.H. (author), Valstar, E.R. (author)

Mechanical loosening of implants is in the majority accompanied with a periprosthetic interface membrane, which has to be removed during revision surgery. The same is true if a minimal invasive (percutaneous) refixation of a loose implant is done. We describe the requirements for a waterjet applicator for interface tissue removal for this...

journal article 2019

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Classical large deviation theorems on complete Riemannian manifolds

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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Personalized support for well-being at work: an overview of the SWELL project

Kraaij, Wessel (author), Verberne, Suzan (author), Koldijk, Saskia (author), de Korte, E.M. (author), van Dantzig, Saskia (author), Sappelli, Maya (author), Hulsebosch, Bob (author), Wabeke, Thymen (author), Neerincx, M.A. (author)

Recent advances in wearable sensor technology and smartphones enable simple and affordable collection of personal analytics. This paper reflects on the lessons learned in the SWELL project that addressed the design of user-centered ICT applications for self-management of vitality in the domain of knowledge workers. These workers often have a...

journal article 2019

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Behavior Change Techniques in mHealth Apps for the Mental and Physical Health of Employees: Systematic Assessment

de Korte, E.M. (author), Wiezer, Noortje (author), Bakhuys Roozeboom, Maartje (author), Vink, P. (author), Kraaij, Wessel (author)

Background: Employees remain at risk of developing physical and mental health problems. To improve the lifestyle, health, and productivity many workplace interventions have been developed. However, not all of these interventions are effective. Mobile and wireless technology to support health behavior change (mobile health [mHealth] apps) is a...

journal article 2018

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Detecting Work Stress in Offices by Combining Unobtrusive Sensors

Neerincx, M.A. (author), Koldijk, Saskia (author), Kraaij, Wessel (author)

Employees often report the experience of stress at work. In the SWELL project we investigate how new context aware pervasive systems can support knowledge workers to diminish stress. The focus of this paper is on developing automatic classifiers to infer working conditions and stress related mental states from a multimodal set of sensor data ...

journal article 2018

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Evaluating an mHealth App for Health and Well-Being at Work: Mixed-Method Qualitative Study

de Korte, E.M. (author), Wiezer, Noortje (author), Janssen, Joris (author), Vink, P. (author), Kraaij, Wessel (author)

Background: To improve workers’ health and well-being, workplace interventions have been developed, but utilization and reach are unsatisfactory, and effects are small. In recent years, new approaches such as mobile health (mHealth) apps are being developed, but the evidence base is poor. Research is needed to examine its potential and to assess...

journal article 2018

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Path-space moderate deviation principles for the random field curie-weiss model

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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Dynamical moderate deviations for the Curie-Weiss model

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