|| Home Page || Courses || Seminar || SSP-2000 || AMS-99 || Preprints || ||

Let X be a jump Markov process with a given q-pair q(x)-q(x,A) (i.e., lim_{t--0}P(t,x,{x})=q(x) and lim_{t--0}P(t,x,A)=q(x,A) for x not in A). Some aspects of the potential theory of X are discussed. For example, we prove:

1. Riesz decomposition. If f is excessive for X, then there is an invariant function h (i.e., P_{t}h=h) and g such that f=h+Ug
2. Equilibrium principle.If B is transient for X, then there exists a unique function f such that P_{B}1=Uf
3. Representative of additive functionals.If A={A_t} is a natural additive functional of X, then A is equivalent to the continuous additive functional B={B_t=\int_{o}^{t}g(X_s)ds} where g(x) is a function determined by the q-pair and A.