:: deftheorem Def30002 defines Adapted_Stochastic_Process FINANCE3:def 15 :
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 Stoch being Stochastic_Process of I,Sigma,Sigma2
for b₇ being Function of I,(set_of_random_variables_on (Sigma,Sigma2)) holds
( b₇ is Adapted_Stochastic_Process of Stoch iff ex k being Filtration of I,Sigma st
for i being Element of I holds RVProcess (Stoch,i) is El_Filtration (i,k),Sigma2 -random_variable-like );