Asymptotics of an Efficient Monte Carlo Estimation for the Transition Density of Diffusion Processes

Osnat Stramer () and Jun Yan ()
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Osnat Stramer: University of Iowa
Jun Yan: University of Iowa

Methodology and Computing in Applied Probability, 2007, vol. 9, issue 4, 483-496

Abstract: Abstract Discretized simulation is widely used to approximate the transition density of discretely observed diffusions. A recently proposed importance sampler, namely modified Brownian bridge, has gained much attention for its high efficiency relative to other samplers. It is unclear for this sampler, however, how to balance the trade-off between the number of imputed values and the number of Monte Carlo simulations under a given computing resource. This paper provides an asymptotically efficient allocation of computing resource to the importance sampling approach with a modified Brownian bridge as importance sampler. The optimal trade-off is established by investigating two types of errors: Euler discretization error and Monte Carlo error. The main results are illustrated with two simulated examples.

Keywords: diffusion process; transition density; Monte Carlo; 60J60; 65C05 (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s11009-006-9006-2

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