  In this article, we introduce Mittag-Leffler L\'evy process and provide two
alternative representations of this process. First, in terms of Laplace
transform of the marginal densities and next as a subordinated stochastic
process. Both these representations are useful in analyzing the properties of
the process. Since integer order moments for this process are not finite, we
obtain fractional order moments. Its density function and corresponding L\'evy
measure density is also obtained. Further, heavy tailed behavior of densities
and stochastic self-similarity of the process is demonstrated. Our results
generalize and complement the results available on Mittag-Leffler distribution
in several directions.
