Please use this identifier to cite or link to this item: https://doi.org/10.1016/j.spa.2012.02.002
Title: Linear variance bounds for particle approximations of time-homogeneous Feynman-Kac formulae
Authors: Whiteley, N.
Kantas, N.
Jasra, A. 
Keywords: Feynman-Kac formulae
Multiplicative drift condition
Non-asymptotic variance
Issue Date: Apr-2012
Citation: Whiteley, N., Kantas, N., Jasra, A. (2012-04). Linear variance bounds for particle approximations of time-homogeneous Feynman-Kac formulae. Stochastic Processes and their Applications 122 (4) : 1840-1865. ScholarBank@NUS Repository. https://doi.org/10.1016/j.spa.2012.02.002
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. © 2011 Elsevier B.V. All rights reserved.
Source Title: Stochastic Processes and their Applications
URI: http://scholarbank.nus.edu.sg/handle/10635/125057
ISSN: 03044149
DOI: 10.1016/j.spa.2012.02.002
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