Spectral Theory for Random Poincaré Maps

DOI10.1137/16M1103816zbMath1374.60149arXiv1611.04869OpenAlexW3105922179MaRDI QIDQ4591197

Manon Baudel, Nils Berglund

Publication date: 13 November 2017

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.04869

zbMATH Keywords

stochastic differential equationmetastabilityspectral theoryperiodic orbitquasi-stationary distributionFredholm theoryreturn mapstochastic exit problemDoob \(h\)-transformrandom Poincaré map

Mathematics Subject Classification ID

Diffusion processes (60J60) Ordinary differential equations and systems with randomness (34F05) Fredholm integral equations (45B05) Transition functions, generators and resolvents (60J35)

Related Items (3)

General criteria for the study of quasi-stationarity ⋮ A random dynamical systems perspective on isochronicity for stochastic oscillations ⋮ Random switching near bifurcations

Cites Work

• Unnamed Item
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• Metastable states, quasi-stationary distributions and soft measures
• Multi-scale metastable dynamics and the asymptotic stationary distribution of perturbed Markov chains
• The Morris-Lecar neuron model embeds a leaky integrate-and-fire model
• The Poincaré map of randomly perturbed periodic motion
• Hunting French ducks in a noisy environment
• Nonequilibrium Markov processes conditioned on large deviations
• The Eyring-Kramers law for Markovian jump processes with symmetries
• Metastability of non-reversible, mean-field Potts model with three spins
• Generalisation of the Eyring-Kramers transition rate formula to irreversible diffusion processes
• Flows in complex networks: theory, algorithms, and application to lennard-Jones cluster rearrangement
• The Poisson kernel for certain degenerate elliptic operators
• The exit problem for small random perturbations of dynamical systems with a hyperbolic fixed point
• Elliptic partial differential equations of second order
• Metastability in reversible diffusion processes. I: Sharp asymptotics for capacities and exit times
• Metastability in reversible diffusion processes. II: Precise asymptotics for small eigenvalues
• Perturbation theory for linear operators.
• Geometric singular perturbation theory for stochastic differential equations.
• Reactive trajectories and the transition path process
• From random Poincaré maps to stochastic mixed-mode-oscillation patterns
• A graph-algorithmic approach for the study of metastability in Markov chains
• Exit asymptotics for small diffusion about an unstable equilibrium
• Towards a theory of transition paths
• Exponential convergence to quasi-stationary distribution and \(Q\)-process
• Analysis of adaptive multilevel splitting algorithms in an idealized case
• Mixed-mode oscillations and interspike interval statistics in the stochastic FitzHugh–Nagumo model
• Kramers' law: Validity, derivations and generalisations
• Normal forms approach to diffusion near hyperbolic equilibria
• Stability of Markovian processes III: Foster–Lyapunov criteria for continuous-time processes
• Extensions of Jentzsch's Theorem
• Adaptive Multilevel Splitting for Rare Event Analysis
• Bursting Oscillations Induced by Small Noise
• Noise-Induced Phenomena in Slow-Fast Dynamical Systems
• On the Noise-Induced Passage through an Unstable Periodic Orbit II: General Case
• Adaptive Multilevel Splitting in Molecular Dynamics Simulations
• Stability, convergence to equilibrium and simulation of non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels
• Metastability
• Ergodicity for a stochastic Hodgkin-Huxley model driven by Ornstein-Uhlenbeck type input

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