looking for a problem's name and possibly algorithm

[Francesco Potortì]

Dear all,

I have a problem which I am sure is very common, but I don't know how it
is usually named.

I have a system with a small number of states (N < 100), which evolves
in discrete time.  I have a state vector indicating the likelihood of
the system to be in any of its possible states.  For each time step,
there can be one of a number of events (M) or no events.  For each
event, or the no-event situation, I have a transition matrix with which
I multiply the state vector to get a new state vector.

So the system evolves at each time step by multiplying the likelihood
state vector by a transition matrix depending on the event happening at
that time step.  At each time, I declare that the system is in state S
where S is the index of the state vector with the highest number.

This may be made more complex by adding some memory: the currect state
vector does not depend only on the immediately past one, but on a small
number of past ones.

What is the official name of such a model, and what are the functions
that I may find useful in Octave's or Octave-forge's arsenal?

Until now, I ma just doing matrix multiplication, and that looks enough,
but onenever knows what's around...

-- 
Francesco Potortì (ricercatore)        Voice:  +39.050.315.3058 (op.2111)
ISTI - Area della ricerca CNR          Mobile: +39.348.8283.107
via G. Moruzzi 1, I-56124 Pisa         Fax:    +39.050.315.2040  
(entrance 20, 1st floor, room C71)     Web:    http://fly.isti.cnr.it