Linear variance bounds for particle approximations of time-homogeneous Feynman-Kac formulae

DOI10.1016/j.spa.2012.02.002zbMath1262.60076arXiv1108.3988OpenAlexW2138086114MaRDI QIDQ424504

Nikolas Kantas, Nick Whiteley, Ajay Jasra

Publication date: 1 June 2012

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1108.3988

zbMATH Keywords

Feynman-Kac formulaMarkov kernelmultiplicative ergodic theoremCox-Ingersoll-Ross processmultiplicative drift conditionnon-asymptotic variance

Mathematics Subject Classification ID

Discrete-time Markov processes on general state spaces (60J05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Ergodic theorems, spectral theory, Markov operators (37A30) Transition functions, generators and resolvents (60J35)

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Cites Work

• Unnamed Item
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• On adaptive resampling strategies for sequential Monte Carlo methods
• Stability of Feynman-Kac formulae with path-dependent potentials
• A sequential Monte Carlo approach to computing tail probabilities in stochastic models
• A nonasymptotic theorem for unnormalized Feynman-Kac particle models
• Tree based functional expansions for Feynman--Kac particle models
• Uniform time average consistency of Monte Carlo particle filters
• Stability and uniform approximation of nonlinear filters using the Hilbert metric and application to particle filters
• Large deviations asymptotics and the spectral theory of multiplicatively regular Markov proces\-ses
• Spectral theory and limit theorems for geometrically ergodic Markov processes
• Polynomial convergence rates of Markov chains
• Large deviation asymptotics and control variates for simulating large functions
• On the stability of sequential Monte Carlo methods in high dimensions
• Sequential Monte Carlo Methods in Practice
• A Theory of the Term Structure of Interest Rates
• Particle Motions in Absorbing Medium with Hard and Soft Obstacles
• Sequential Monte Carlo Methods for Option Pricing
• General Irreducible Markov Chains and Non-Negative Operators
• Markov Chains and Stochastic Stability
• Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups
• Sequential Monte Carlo methods for diffusion processes
• Risk-Sensitive Control of Discrete-Time Markov Processes with Infinite Horizon
• On the stability of interacting processes with applications to filtering and genetic algorithms