Stateful means the computer or program keeps track of the state of interaction, usually by setting values in a storage field designated for that purpose. Stateless means there is no record of previous interactions and each interaction request has to be handled based entirely on information that comes with it.
Most BREs today are deployed as “decision services”, and are used in “stateless” transactions to make “decisions” as a part of a business process. A CEP application is instead processing multiple event streams and sources over time, which requires a “stateful” rule service optimized for long running. This is an important distinction, as a stateful BRE for long-running processes needs to have failover support - the ability to cache its working memory for application restarting or distribution. And of course long-running processes need to be very particular over issues like memory handling - no memory leaks allowed!
The one, really big, difference between Complex Event Processing and traditional BRMS tools is that the former is loosely associated with EDA and decisions that are based on multiple events, whereas the latter is more associated with conventional request-reply SOA and automating decisions made in managed business processes.
M. zur Muehlen, M. Indulska, and K. Kittel. 19th Australasian Conference on Information Systems (ACIS 2008), Christchurch, New Zealand, Australasian Computer Society, (2008)
J. Schiefer, S. Rozsnyai, C. Rauscher, and G. Saurer. DEBS '07: Proceedings of the 2007 inaugural international conference on Distributed event-based systems, page 198--205. New York, NY, USA, ACM, (2007)
M. zur Muehlen, M. Indulska, and G. Kamp. EDOCW '07: Proceedings of the 2007 Eleventh International IEEE EDOC Conference Workshop, page 189--196. Washington, DC, USA, IEEE Computer Society, (2007)