STOPPING GAMES FOR SYMMETRIC MARKOV PROCESSES

Abstract: Let be a Dirichlet form corresponding to a symmetric Markov process
acting on a state space Let and , be quasi-continuous
elements of the corresponding Dirichlet space , and a quasi-continuous solution of the
variational inequality

where

and

for all

. It is shown in the
paper that if

is defined for all

and all stopping times

and

by

then
for quasi-every

we have

Moreover, for quasi-every

the pair

such that

is
the saddle point of the game

for
all stopping times

and quasi-every

.

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -