Properties of arbitrary truncated Levy flight are investigated by method of cumulant approach  . The set of cumulants that characterized an arbitrary truncated Levy distribution is found and their shape of truncation dependence is defined . The influence of truncation shape on the properties of Gaussian and Levy regimes of process is investigated.
The problem of an arbitrary truncated Levy flight description using the method of cumulant approach has been solved . The set of cumulants of the truncated Levy distribution given the assumption of arbitrary truncation has been found . The influence of truncation shape on the truncated Levy flight properties in the Gaussian and the Levy regimes has been investigated.
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