Recently (~10 years ago), Kuchler&Tappe have set up a new stochastic process called Bilateral Gamma process. This process is defined through its increments:
$$\forall t\geq s, X_t-X_s\sim \Gamma_{BG}(\alpha_+(t-s), \lambda_+, \alpha_-(t-s), \lambda_-)$$
where:
$$\Gamma_{BG}(\alpha_+, \lambda_+, \alpha_-, \lambda_-) =\Gamma(\alpha_+, \lambda_+)*\Gamma( \alpha_-, \lambda_-). $$
My question is maybe naive but, from this definition: how can we see that $X$ is a pure jump process ?
Thank you very much !
