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I would like to create a stochastic process connected with Normal Inverse Gaussian distribution. My process starts from price P_0 (I know that in the Brownian motion there is a first point from definition that it should start from 0, but I think it is just a notation. This process is generated by following formula:

$Y_t = Y_{t-1} + Y_{t-1}e_t$

Where: $e_t \sim NIG(\alpha, \beta, \gamma, \delta)$

How could I check if this process is a Brownian motion? Or it is not.

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