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

Nick P Whiteley, Nikolas Kantas, Ajay Jasra

Research output: Contribution to journalArticle (Academic Journal)peer-review

11 Citations (Scopus)

Abstract


This article establishes sufficient conditions for a linear-in-time bound on the non-asymptotic variance for particle approximations of time-homogeneous Feynman–Kac formulae. These formulae appear in a wide variety of applications including option pricing in finance and risk sensitive control in engineering. In direct Monte Carlo approximation of these formulae, the non-asymptotic variance typically increases at an exponential rate in the time parameter. It is shown that a linear bound holds when a non-negative kernel, defined by the logarithmic potential function and Markov kernel which specify the Feynman–Kac model, satisfies a type of multiplicative drift condition and other regularity assumptions. Examples illustrate that these conditions are general and flexible enough to accommodate two rather extreme cases, which can occur in the context of a non-compact state space: (1) when the potential function is bounded above, not bounded below and the Markov kernel is not ergodic; and (2) when the potential function is not bounded above, but the Markov kernel itself satisfies a multiplicative drift condition.
Original languageEnglish
Pages (from-to)1840-1865
Number of pages26
JournalStochastic Processes and their Applications
Volume122
Issue number4
DOIs
Publication statusPublished - Apr 2012

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