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The criterion and sufficient condition for the existence of moments of one-parameter increasing predictable processes is presented in terms of an associated potential. The estimates of moments of special functional connected with two-parameter increasing predictable processes are given in the case when the associated potential is bounded. The application of these estimates to the local time for purely discontinuous strong martingales in the plane is also presented

Existence of moments of increasing predictable processes associated with one‐ and two‐parameter potentials