紀要論文

紀要論文

text

Osaka Journal of Mathematics. 2014, 51(2), p. 337-358

INFINITE MARKOV PARTICLE SYSTEMS ASSOCIATED WITH ABSORBING STABLE MOTION ON A HALF SPACE

Hiraba, Seiji

Osaka University and Osaka City University, Departments of Mathematics

英語

text

2014-04

In general, for a Markov process which does not have an invariant measure, it is possible to realize a stationary Markov process with the same transition probability by extending the probability space and by adding new paths which are born at random times. The distribution (which may not be a probability measure) is called a Kuznetsov measure. By using this measure we can construct a stationary Markov particle system, which is called an equilibrium process with immigration. This particle system can be decomposed as a sum of the original part and the immigration part (see [2]). In the present paper, we consider an absorbing stable motion on a half space H, i.e., a time-changed absorbing Brownian motion on H by an increasing strictly stable process. We first give the martingale characterization of the particle system. Secondly, we discuss the finiteness of the number of particles near the boundary of the immigration part. (cf. [2], [3], [4].)

10.18910/29201

29201

INFINITE MARKOV PARTICLE SYSTEMS ASSOCIATED WITH ABSORBING STABLE MOTION ON A HALF SPACE

Hiraba, Seiji

Osaka University and Osaka City University, Departments of Mathematics

英語

2014-04

Osaka Journal of Mathematics

51

2

337

358

https://hdl.handle.net/11094/29201

10.18910/29201

https://doi.org/10.18910/29201