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• W3100143746 abstract "This paper presents a new approach to the analysis of mixed processes [X_t=B_t+G_t,qquad tin[0,T],] where $B_t$ is a Brownian motion and $G_t$ is an independent centered Gaussian process. We obtain a new canonical innovation representation of $X$, using linear filtering theory. When the kernel [K(s,t)=frac{partial^2}{partial s,partial t}mathbb{E}G_tG_s,qquad sne t] has a weak singularity on the diagonal, our results generalize the classical innovation formulas beyond the square integrable setting. For kernels with stronger singularity, our approach is applicable to processes with additional fractional structure, including the mixed fractional Brownian motion from mathematical finance. We show how previously-known measure equivalence relations and semimartingale properties follow from our canonical representation in a unified way, and complement them with new formulas for Radon-Nikodym densities." @default.
• W3100143746 created "2020-11-23" @default.
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• W3100143746 date "2016-07-01" @default.
• W3100143746 modified "2023-10-10" @default.
• W3100143746 title "Mixed Gaussian processes: A filtering approach" @default.
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• W3100143746 doi "https://doi.org/10.1214/15-aop1041" @default.
• W3100143746 hasPublicationYear "2016" @default.
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