A marked point process with mark space 
is a double sequence
 |
of 
-valued
random variables and 
-valued random variables 
defined on a probability
space 
such that 
is a simple point process (SPP) and:
1. 
for 
;
2. 
for 
.
Here, 
denotes probability, 
denotes the so-called irrelevant mark which is used to
describe the mark of an event that never occurs, and 
.
This definition is similar to the definition of an SPP in that it describes a sequence of time points marking the occurrence of events. The difference is that these events
may be of different types where the type (i.e., the mark) of the 
th event is denoted by 
. Note that, because of the inclusion of the irrelevant mark
,
marking will assign values 
for all 
--even when 
, i.e., when the 
th event never occurs (Jacobsen 2006).
