THE LIL FOR LOCALLY SQUARE INTEGRABLE MARTINGALE

In this paper, we derive the LIL for continuous-time locally square integrable martingale whose jumps grow at a controlled rate. The results generalize Stout's LIL for disorete-time locally square integrable martingale.
Let (\Omega, F, P) be a probability space with a filtration, \left\F_t, t \geqslant 0\right\ F_0=\\phi, \Omega\; Let M=\left(M_t, t \geqslant 0\right) be a locally square integrable martingale, M_0=0,\langle M\rangle be the compensator of M^2, we have the following Theorem 1. Let \left\k_t, t \geqslant 0\right\ be \left\F_t\right\ predicatable, sappose for some constant 0