:: deftheorem defines -stoch_proc_wrt_to_Filtration FINANCE3:def 17 :
for Omega, Omega2 being non empty set
for Sigma being SigmaField of Omega
for Sigma2 being SigmaField of Omega2
for I being non empty real-membered set
for MyFunc being ManySortedSigmaField of I,Sigma
for Stoch being Stochastic_Process of I,Sigma,Sigma2 holds
( Stoch is MyFunc -stoch_proc_wrt_to_Filtration iff for i being Element of I holds RVProcess (Stoch,i) is El_Filtration (i,MyFunc),Sigma2 -random_variable-like );