Abstract
Kazamaki has shown that if (M~)nz1 M are BMO martingales with continuous paths and lim M' = M in BMO, then e(Mf) converges in Al to &(M), where 6(M) denotes the stochastic exponential of M. While Kazamaki's result does not extend to the right continuous case, it does extend locally. It is shown here that if M', M are semimartingales and M' converges locally in A (a semimartingale BMO-type norm) to M then X' converges locally in AT (1 _ p < 0o) to X, where X', X are resepctively solutions of stochastic integral equations with Lipschitz-type coefficients and differentials dM', dM. (The coefficients are also allowed to vary.) This is a stronger stability than usually holds for solutions of stochastic integral equations, reflecting the strength of the Y norm.
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