Stationary marked point processes : an intuitive approach /
Karl Sigman.
- New York : Chapman & Hall, c1995.
- xiii, 200 p. : ill. ; 24 cm.
- Stochastic modeling .
Includes bibliographical references (p. [191]-195) and index.
Preface Marked Point Processes Random Marked Point Processes An Interlude: Constructing Stationary Versions Further Topics on Stationarity Processes Jointly with Marked Point Processes Applications to Queues Topology Measure Theory Metric Spaces The Space of Marked Point Processes References Index
Taking an applied point of view, this book provides an accessible introduction to the theory of stationary random marked point processes on the non-negative real line. The reader will be able to gain an intuitive understanding of stationary marked point processes and be able to apply the theory to stochastic modeling. The emphasis is on time averages and asymptotic stationarity. Proofs of the main results are given using shift-coupling methods and measure theory is kept to a minimum. Examples and exercises are given involving explicit construction of time and event stationary versions, using the 'inspection paradox' as an intuitive guide. The Rate Conservation Law is given and used in applications to queueing theory. The prerequisites are a background in probability theory and stochastic processes up to conditional expectation.