= Solution
A real <Lévy process> is a real-valued <stochastic process> $(X_t)_{t\geq0}$ with the following properties:
* $X_0=0$ <almost surely>.
* It has <independent increments>: increments over disjoint ordered time intervals are independent.
* It has <stationary increments>: $X_{s+t}-X_s$ has the same law as $X_t$ for $s,t\geq0$.
* It has <stochastic continuity>: $X_s\to X_t$ in probability as $s\to t$.
One convention also includes <càdlàg> paths in the definition. Equivalently, under the intrinsic definition above one chooses the <càdlàg modification>, which exists for such a <stochastic process>. Thus the usual working version of a <Lévy process> has <right-continuous> paths with left limits. There is no assumption of finite <moments> or continuous paths.
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