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A deterministic model/approach has predefined results like we know the possible input.On the other hand a stochastic model/approach has a real time input so that it is not known priorly.A possible example can be the diffeence between digital filters like IIR/FIR and Kalman filters.
deterministic = non-random (everything values, behavior known exactly)
stochastic = random (something are not known exactly, only explained in terms of probabilities)
stochastic process is more difficult to be modeled and simulated..........and in complex systems u may have to neglect some variables to be able to use the model
Exactly modeling a stochastic model involves difficulty as only here the adaptation is brought in.whenever the system is said to possess adaptive nature framing a model to explain its behaviour becomes tougher.The best example for adaptation is modeling synapse in neurons which is subjected to adaptation.
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