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arXiv · 1911.10972

On unbiased simulations of stochastic bridges conditioned on extrema

Andrew Schaug·Harish Chandra
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Abstract

Stochastic bridges are commonly used to impute missing data with a lower sampling rate to generate data with a higher sampling rate, while preserving key properties of the dynamics involved in an unbiased way. While the generation of Brownian bridges and Ornstein-Uhlenbeck bridges is well understood, unbiased generation of such stochastic bridges subject to a given extremum has been less explored in the literature. After a review of known results, we compare two algorithms for generating Brownian bridges constrained to a given extremum, one of which generalises to other diffusions. We further apply this to generate unbiased Ornstein-Uhlenbeck bridges and unconstrained processes, both constrained to a given extremum, along with more tractable numerical approximations of these algorithms. Finally, we consider the case of drift, and applications to geometric Brownian motions.

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Andrew Schaug, Harish Chandra. 2019-11-25. On unbiased simulations of stochastic bridges conditioned on extrema. https://arxiv.org/abs/1911.10972

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