Variance Gamma Process
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High Quality Content by WIKIPEDIA articles! In the theory of stochastic processes, a part of the mathematical theory of probability, the variance gamma process (VG), also known as Laplace motion, is a Lévy process determined by a random time change. The process has finite moments distinguishing it from many Lévy processes. There is no diffusion component in the VG process and it is thus a pure jump Lévy process. The increments are independent and follow a Laplace distribution. There are several representations of the VG process that relate it to other processes. It can for example be written…mehr

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High Quality Content by WIKIPEDIA articles! In the theory of stochastic processes, a part of the mathematical theory of probability, the variance gamma process (VG), also known as Laplace motion, is a Lévy process determined by a random time change. The process has finite moments distinguishing it from many Lévy processes. There is no diffusion component in the VG process and it is thus a pure jump Lévy process. The increments are independent and follow a Laplace distribution. There are several representations of the VG process that relate it to other processes. It can for example be written as a Brownian motion subjected to a random time change following a gamma process. Since the VG process is of finite variation it can be written as the difference of two independent gamma processes. Alternatively it can be approximated by a compound Poisson process that leads to a representation with explicitly given (independent) jumps and their locations. This last characterization gives an understanding of the strucuture of the sample path with location and sizes of jumps..