TABLE OF CONTENTS We briefly mention some results on solving stochastic differential equations.
One type of existence result for stochastic differential equations is the following.
Let b be the n-dimensional Anderson s Brownian motion with filtration {F t } t ?[0,1]. Let
be bounded and measurable. Suppose that the determinant of g is uniformly bounded away from 0, i. e. for some 
,
Then for any F 0 -measurable x 0, there is a continuous adapted process x satisfying
Another type is some thing like this:
(Still using the same n-dimensional b and the same filtration.) Let
such that f( ?, s, ), g( ?, s, ) are bounded adapted processes with values in the space of continuous functions 
and 
respectively. Then for any F 0 -measurable x 0, there is a continuous adapted process x satisfying
It should be noted that the above gives strong solutions in the sense that the same filtration works for any f, g in the theorem. This is a feature of Anderson s Brownian motion that distinguish it from standard Brownian motion and filtrations. Very often, standard results produce only weak solutions, i.e. the choice of filtration depends on the particular f and g.
For complete proofs and discussions, as well as generalizations, see [Albeverio et al., 1986], [Keisler, 1984], [Lindstr m, 1980] and [Stroyan and Bayod, 1986]. See also [Hoover and Perkins, 1983] for dealing with equations...
