**Seiji Hiraba**. **Source: **Osaka Journal of Mathematics, Volume 51, Number 2, 337--359.**Abstract:**

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].)

**Setki tysięcy abstraktów z prac naukowych, które ukazały się w okresie styczeń 2014 r. - 5 października 2014 r. i wiele więcej.**