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• W2962918342 abstract "Subordinating a multivariate Lévy process, the subordinate, with a univariate subordinator gives rise to a pathwise construction of a new Lévy process, provided the subordinator and the subordinate are independent processes. The variance-gamma model in finance was generated accordingly from a Brownian motion and a gamma process. Alternatively, multivariate subordination can be used to create Lévy processes, but this requires the subordinate to have independent components. In this paper, we show that there exists another operation acting on pairs $(T,X)$ of Lévy processes which creates a Lévy process $Xodot T$. Here, $T$ is a subordinator, but $X$ is an arbitrary Lévy process with possibly dependent components. We show that this method is an extension of both univariate and multivariate subordination and provide two applications. We illustrate our methods giving a weak formulation of the variance-$boldsymbol{alpha}$-gamma process that exhibits a wider range of dependence than using traditional subordination. Also, the variance generalised gamma convolution class of Lévy processes formed by subordinating Brownian motion with Thorin subordinators is further extended using weak subordination." @default.
• W2962918342 created "2019-07-30" @default.
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• W2962918342 date "2019-02-01" @default.
• W2962918342 modified "2023-09-26" @default.
• W2962918342 title "Weak subordination of multivariate Lévy processes and variance generalised gamma convolutions" @default.
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• W2962918342 doi "https://doi.org/10.3150/17-bej1004" @default.
• W2962918342 hasPublicationYear "2019" @default.
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