:: deftheorem Def30002 defines Adapted_Stochastic_Process FINANCE3:def 16 :
for Omega, Omega2 being non empty set
for Sigma being SigmaField of Omega
for Sigma2 being SigmaField of Omega2
for I being non empty Subset of REAL
for Prob being Probability of Sigma
for Stoch being Stochastic_Process of I,Sigma,Sigma2,Prob
for b₈ being Function of I,(set_of_random_variables_on (Sigma,Sigma2)) holds
( b₈ is Adapted_Stochastic_Process of I,Sigma,Sigma2,Prob,Stoch iff ex k being Filtration of I,Sigma st
for i being Element of I holds RVProcess (Stoch,i) is_random_variable_on El_Filtration (i,k),Sigma2 );