CHAPTER 4
CONTINUOUS-TIME STOCHASTIC PROCESSES
4.1 GENERAL DESCRIPTION OF CONTINUOUS-TIME STOCHASTIC PROCESSES
Just as in the discrete-time case, the description of a continuous-time stochastic process begins with a time-dependent information structure or filtration {
, 0 ≤ t ≤ T}, on a probability space 
. The information structure {} satisfies the usual conditions:
(i) For each t, is an information structure containing no more information than 
, and it represents the information up to time t ;
(ii) If s < t, 
contains no more information than , i.e. all the events in are events in . In ...
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