ar.e gratefully acknowledged, and suggestions from two referees on an earlier version have provided many improvements. E. Burmeister is also grateful for research support from Duke University where some of this work was completed.
An a s y m p t o t i c d i s t r i b u t i o n t h e o r y f o r t h e s t a t e e s t i m a t e from a Kalman f i l t e r i n t h e a b s e n c e o f t h e u s u a l G a u s s i a n a s s u m p t i o n i s p r e s e n t e d . I t i s found t h a t t h e s t a b i l i t y p r o p e r t i e s o f thc s t a t e t r a n s i t i o n m a t r i x p l a y a k e y r o l e i n t h e d i s t r i b u t i o n t h e o r ) . S p e c i f i c a l l y , when t h e s t a t e e q u a t i o n i s n e u t r a l l y s t a b l e ( i . e . , b o r d e r l i n e s t a b l e -u n s t a b l e ) t h e s t a t e e s t i m a t e i s a s y m p t o t i t a l l y n o r m a l when t h e random t e r m s i n t h e model h a v e a r b i t r a r y d i s t r ib u t i o n s . T h i s c a s e i n c l u d e s t h e p o p u l a r random w a l k s t a t e equat i o n . However, when t h e s t a t e e q u a t i o n i s e i t h e r s t a b l e o r u n s t a b l e , a t l e a s t some o f t h e random t e r m s i n t h e model must b e n o r m a l l y d i s t r i b u t e d beyond some f i n i t e t i m e b e f o r e t h e s t a t e e s t i m a t e i s a s y m p t o t i c a l l y n o r m a l .
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