Generalized Gaussian bridges

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• 作者：Tommi Sottinen ; ^{tommi.sottinen@uva.fi" class="auth_mail} ; ^{tommi.sottinen@uwasa.fi" class="auth_mail} ; Adil Yazigi ^{adil.yazigi@uwasa.fi" class="auth_mail}
• 关键词：60G15 ; 60G22 ; 91G80
• 刊名：Stochastic Processes and their Applications
• 出版年：September 2014
• 年：2014
• 卷：124
• 期：9
• 页码：3084-3105
• 全文大小：272 K

文摘

A generalized bridge is a stochastic process that is conditioned on 914000878&_mathId=si1.gif&_user=111111111&_pii=S0304414914000878&_rdoc=1&_issn=03044149&md5=5649ceae3c31cee32fd471750504acad" title="Click to view the MathML source">N$N$ 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.