The chaotic-representation property for a class of normal martingales

Suppose Z=(Zt)t>/=0 is a normal martingale which satisfies the structure equation ... . By adapting and extending techniques due to Parthasarathy and to Kurtz, it is shown that, if a is locally bounded and beta has values in the interval [-2,0], the process Z is unique in law, possesses the chaotic-representation property and is strongly Markovian (in an appropriate sense). If also beta is bounded away from the endpoints 0 and 2 on every compact subinterval of [0,infinity] then Z is shown to have locally bounded trajectories, a variation on a result of Russo and Vallois.