We examine a piecewise deterministic Markov process, whose whole randomness stems from the jumps, which occur at the random time points according to a Poisson process, and whose post-jump locations are attained by randomly selected transformations of the pre-jumps states. Between the jumps, the process is deterministically driven by a continuous semiflow. The aim of the paper is to establish the continuous dependence of the invariant measure of this process on the jump intensity.

1.
M.
Davis
,
J.
Roy
.
Statist. Soc. Ser. B
46
,
353
388
(
1984
).
2.
B.
Cloez
 et al.,
ESAIM: Proceedings and Surveys
60
,
225
245
(
2017
).
3.
M.
Mackey
,
M.
Tyran-Kamińska
, and
R.
Yvinec
,
SIAM J. Appl. Math.
73
,
1830
1852
(
2013
).
4.
O.
Costa
and
F.
Dufour
,
SIAM J. Control Optim.
47
,
1053
1077
(
2008
).
5.
D.
Czapla
,
K.
Horbacz
, and
H.
Wojewódka
, accepted in
Stoch. Proc. Appl.
, arXiv:1707.06489v3 (
2018
).
6.
D.
Czapla
and
J.
Kubieniec
,
Dynamical Systems
34
,
130
156
(
2019
).
7.
A.
Lasota
and
M.
Mackey
,
J. Math. Biol.
38
,
241
261
(
1999
).
8.
R.
Dudley
,
Stud. Math.
27
,
251
268
(
1966
).
9.
A.
Lasota
,
Lecture Notes in Phys. (Springer Verlag)
457
,
235
255
(
1995
).
10.
D.
Worm
, PhD. thesis,
Leiden University
, https://openaccess.leidenuniv.nl/handle/1887/15948 (
2010
).
11.
W.
Rudin
,
Principles of mathematical analysis
(
McGraw-Hill, Inc
.,
New York
,
1976
).
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