TY - GEN
T1 - Extending Markov processes in weak duality by poisson point processes of excursions
AU - Chen, Zhen Qing
AU - Fukushima, Masatoshi
AU - Ying, Jiangang
PY - 2007
Y1 - 2007
N2 - Let a be a non-isolated point of a topological space E. Suppose we are given standard processes X0 and XC0 on Eo = E \ {a} in weak duality with respect to a σ-finite measure m on E0 which are of no killings inside E0 but approachable to a. We first show that their extensions X and X̂ to E admitting no sojourn at a and keeping the weak duality are uniquely determined by the approaching probabilities of X0, X̂0 and m up to a non-negative constant δ0representing the killing rate of X at a. We then construct, starting from X0, such X by piecing together returning excursions around a and a possible non-returning excursion including the instant killing. This extends a recent result by M. Fukushima and H. Tanaka [16] which treats the case where X0, X are m-symmetric diffusions and X admits no sojourn nor killing at a. Typical examples of jump type symmetric Markov processes and non-symmetric diffusions on Euclidean domains are given at the end of the paper.
AB - Let a be a non-isolated point of a topological space E. Suppose we are given standard processes X0 and XC0 on Eo = E \ {a} in weak duality with respect to a σ-finite measure m on E0 which are of no killings inside E0 but approachable to a. We first show that their extensions X and X̂ to E admitting no sojourn at a and keeping the weak duality are uniquely determined by the approaching probabilities of X0, X̂0 and m up to a non-negative constant δ0representing the killing rate of X at a. We then construct, starting from X0, such X by piecing together returning excursions around a and a possible non-returning excursion including the instant killing. This extends a recent result by M. Fukushima and H. Tanaka [16] which treats the case where X0, X are m-symmetric diffusions and X admits no sojourn nor killing at a. Typical examples of jump type symmetric Markov processes and non-symmetric diffusions on Euclidean domains are given at the end of the paper.
UR - https://www.scopus.com/pages/publications/84883606664
U2 - 10.1007/978-3-540-70847-6_7
DO - 10.1007/978-3-540-70847-6_7
M3 - Conference contribution
AN - SCOPUS:84883606664
SN - 3540708464
SN - 9783540708469
T3 - Stochastic Analysis and Applications: The Abel Symposium 2005 - Proceedings of the 2nd Abel Symposium, Held in Honor of Kiyosi Ito
SP - 153
EP - 196
BT - Stochastic Analysis and Applications
PB - Springer Verlag
T2 - 2nd Abel Symposium 2005: Stochastic Analysis and Applications
Y2 - 29 July 2005 through 4 August 2005
ER -