33 citations · 208 across the 32 of their papers we have counts for
33 papers
A Strict Comparison Principle for Integro-Differential Hamilton-Jacobi-Bellman Equations on Domains with Boundary
Serena Della Corte, Fabian Fuchs, Richard C. Kraaij +1
This work provides a comparison principle for viscosity solutions to boundary value problems on (partially) bounded, cylindrical spaces. The comparison principle is based on a test…
A comparison principle based on couplings of partial integro-differential operators
Serena Della Corte, Fabian Fuchs, Richard C. Kraaij +1
This paper is concerned with a comparison principle for viscosity solutions to Hamilton-Jacobi (HJ), -Bellman (HJB), and -Isaacs (HJI) equations for general classes of partial inte…
Large deviations for slow-fast processes on connected complete Riemannian manifolds
Yanyan Hu, Richard C. Kraaij, Fubao Xi
We consider a class of slow-fast processes on a connected complete Riemannian manifold .The limiting dynamics as the scale separation goes to is governed by the averagi…
Hamilton--Jacobi equations for Wasserstein controlled gradient flows: existence of viscosity solutions
Giovanni Conforti, Richard C. Kraaij, Luca Tamanini +1
This work is the third part of a program initiated in arXiv:2111.13258, arXiv:2302.06571 aiming at the development of an intrinsic geometric well-posedness theory for Hamilton-Jaco…
Well-posedness of a Hamilton-Jacobi-Bellman equation in the strong coupling regime
Serena Della Corte, Richard C. Kraaij
We prove comparison principle for viscosity solutions of a Hamilton-Jacobi-Bellman equation in a strong coupling regime considering a stationary and a time-dependent version of the…
Large deviations for Cox-Ingersoll-Ross processes with state-dependent fast switching
Yanyan Hu, Richard C. Kraaij, Fubao Xi
We study the large deviations for Cox-Ingersoll-Ross (CIR) processes with small noise and state-dependent fast switching via associated Hamilton-Jacobi equations. As the separation…
Hamilton--Jacobi equations for controlled gradient flows: cylindrical test functions
Giovanni Conforti, Richard C. Kraaij, Daniela Tonon
This work is the second part of a program initiated in arXiv:2111.13258 aiming at the development of an intrinsic geometric well-posedness theory for Hamilton-Jacobi equations rela…
Large deviations for Markov processes with switching and homogenisation via Hamilton-Jacobi-Bellman equations
Serena Della Corte, Richard C. Kraaij
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…
Hamilton--Jacobi equations for controlled gradient flows: the comparison principle
Giovanni Conforti, Richard Kraaij, Daniela Tonon
Motivated by recent developments in the fields of large deviations for interacting particle system and mean field control, we establish a comparison principle for the Hamilton--Jac…
A large deviation principle for Markovian slow-fast systems
Richard C. Kraaij, Mikola C. Schlottke
We prove pathwise large deviation principles of slow variables in slow-fast systems in the limit of time-scale separation tending to infinity. In the limit regime we consider, the…
Comparison Principle for Hamilton-Jacobi-Bellman Equations via a Bootstrapping Procedure
Richard C. Kraaij, Mikola C. Schlottke
We study the well-posedness of Hamilton-Jacobi-Bellman equations on subsets of in a context without boundary conditions. The Hamiltonian is given as the supremum ove…
The exponential resolvent of a Markov process and large deviations for Markov processes via Hamilton-Jacobi equations
Richard C. Kraaij
We study the Hamilton-Jacobi equation f - lambda Hf = h, where H f = e^{-f}Ae^f and where A is an operator that corresponds to a well-posed martingale problem. We identify an opera…
Strict continuity of the transition semigroup for the solution of a well-posed martingale problem
Richard C. Kraaij
In this note we connect the notion of solutions of a martingale problem to the notion of a strongly continuous and locally equi-continuous semigroup on the space of bounded continu…
Gamma convergence on path-spaces via convergence of viscosity solutions of Hamilton-Jacobi equations
Richard C. Kraaij
We establish a framework that allows to prove Gamma-converge of functionals of Lagrangian form on spaces of trajectories based on convergence of viscosity solutions of associated H…
A general convergence result for viscosity solutions of Hamilton-Jacobi equations and non-linear semigroups
Richard C. Kraaij
We extend the Barles-Perthame procedure of semi-relaxed limits of viscosity solutions of Hamilton-Jacobi equations of the type f - lambda H f = h. The convergence result allows for…
Path-space moderate deviations for a class of Curie-Weiss models with dissipation
Francesca Collet, Richard C. Kraaij
We modify the Glauber dynamics of the Curie-Weiss model with dissipation in Dai Pra, Fischer, Regoli[2013] by considering arbitrary transition rates and we analyze the phase-portra…
A generator approach to stochastic monotonicity and propagation of order
Richard C. Kraaij, Moritz Schauer
We study stochastic monotonicity and propagation of order for Markov processes with respect to stochastic integral orders characterized by cones of functions satisfying …
Well-posedness of Hamilton-Jacobi equations in population dynamics and applications to large deviations
Richard C. Kraaij, Louis Mahé
We prove Freidlin-Wentzell type large deviation principles for various rescaled models in populations dynamics that have immigration and possibly harvesting: birth-death processes,…
Classical large deviations theorems on complete Riemannian manifolds
Richard C. Kraaij, Frank Redig, Rik Versendaal
We generalize classical large deviations theorems to the setting of complete Riemannian manifolds. We prove the analogue of Mogulskii's theorem for geodesic random walks via a gene…
Path-space moderate deviations for a Curie-Weiss model of self-organized criticality
Francesca Collet, Matthias Gorny, Richard Clemens Kraaij
The dynamical Curie-Weiss model of self-organized criticality (SOC) was introduced in \cite{Gor17} and it is derived from the classical generalized Curie-Weiss by imposing a micros…
Fluctuation symmetry leads to GENERIC equations with non-quadratic dissipation
Richard C. Kraaij, Alexandre Lazarescu, Christian Maes +1
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 demonst…
A Hamilton-Jacobi point of view on mean-field Gibbs-non-Gibbs transitions
Richard C. Kraaij, Frank Redig, Willem B. van Zuijlen
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 transitio…
Flux large deviations of weakly interacting jump processes via well-posedness of an associated Hamilton-Jacobi equation
Richard C. Kraaij
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…
Gibbs-non-Gibbs transition in the fuzzy Potts models with a Kac-type interaction: Closing the Ising gap
Florian Henning, Richard C. Kraaij, Christof Kuelske
We complete the investigation of the Gibbs properties of the fuzzy Potts model on the d-dimensional torus with Kac interaction which was started by Jahnel and one of the authors. A…