Generalized Gaussian bridges

Tommi Sottinen () and Adil Yazigi

Stochastic Processes and their Applications, 2014, vol. 124, issue 9, 3084-3105

Abstract: A generalized bridge is a stochastic process that is conditioned on N linear functionals of its path. We consider two types of representations: orthogonal and canonical. The orthogonal representation is constructed from the entire path of the process. Thus, the future knowledge of the path is needed. In the canonical representation the filtrations of the bridge and the underlying process coincide. The canonical representation is provided for prediction-invertible Gaussian processes. All martingales are trivially prediction-invertible. A typical non-semimartingale example of a prediction-invertible Gaussian process is the fractional Brownian motion. We apply the canonical bridges to insider trading.

Keywords: Canonical representation; Enlargement of filtration; Fractional Brownian motion; Gaussian process; Gaussian bridge; Hitsuda representation; Insider trading; Orthogonal representation; Prediction-invertible process; Volterra process (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (7)

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Working Paper: Generalized Gaussian Bridges (2013)
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DOI: 10.1016/j.spa.2014.04.002

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