33 citations · 208 across the 32 of their papers we have counts for
19 papers · 1 filter
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…
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…
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…
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…
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…
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…
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…
Path-space moderate deviation principles for the random field Curie-Weiss model
Francesca Collet, Richard C. Kraaij
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…
A large deviation perspective on exponential decay of entropy and lower bounds on the Ricci-curvature
Richard C. Kraaij
We offer a new point of view on the (Modified) Log-Sobolev inequality and lower bounds on the Ricci-curvature in the setting where the dynamics are obtained as the limit of Markov…
Dynamical moderate deviations for the Curie-Weiss model
Francesca Collet, Richard Kraaij
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…
Large deviations for Markov jump processes with mean-field interaction via the comparison principle for an associated Hamilton-Jacobi equation
Richard Kraaij
We prove the large deviation principle for the trajectory of a broad class of mean field interacting Markov jump processes via a general analytic approach based on viscosity soluti…
Stationary product measures for conservative particle systems and ergodicity criteria
Richard Kraaij
We study conservative particle systems on W^S, where S is countable and W = {0, ..., N} or the natural numbers. The rate of a particle moving from site x to site y is given by p(x,…