EXISTENCE AND NON-EXISTENCE OF SOLUTIONS OF
ONE-DIMENSIONAL STOCHASTIC EQUATIONS
Abstract: We consider the one-dimensional stochastic equation
for a
continuous local martingale
with square variation
and measurable drift and
diffusion coefficients
and
The main purpose of this paper is to derive a necessary
condition for the existence of a solution
starting from
As a result, we construct a
diffusion coefficient
such that the above stochastic equation has no solution
whatever
the initial value
and the non-zero, say, continuous drift coefficient
might
be.
1991 AMS Mathematics Subject Classification: 60H10, 60G44.
Key words and phrases: Stochastic equations, continuous local martingales,
non-existence, local time.