:: deftheorem defines Predictable_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, J being non empty Subset of NAT
for Stoch being Stochastic_Process of In (J,(bool REAL)),Sigma,Sigma2
for b₈ being Function of J,(set_of_random_variables_on (Sigma,Sigma2)) holds
( b₈ is Predictable_Stochastic_Process of I,J,Sigma,Sigma2,Stoch iff ex k being Filtration of In (I,(bool REAL)),Sigma st
for j being Element of In (J,(bool REAL))
for i being Element of In (I,(bool REAL)) st j - 1 = i holds
RVProcess (Stoch,j) is El_Filtration (i,k),Sigma2 -random_variable-like );