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 writte...
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..
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