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Words from Wiki that I agree with. Basically, stochastic systems are likely systems where our modeling fails because there's so much parameter space to search through that it's unlikely we'll find the parameter range in which a deterministic model exhibits chaos. Thus it appears random to us (due to a lack of a priori knowledge) and stochastic modeling is more time-efficient.
Wiki's references (appealing to authorities of philosophy and math):
Werndl, Charlotte (2009). Are Deterministic Descriptions and Indeterministic Descriptions Observationally Equivalent?. Studies in History and Philosophy of Modern Physics 40, 232-242.
Werndl, Charlotte (2009). Deterministic Versus Indeterministic Descriptions: Not That Different After All?. In: A. Hieke and H. Leitgeb (eds), Reduction, Abstraction, Analysis, Proceedings of the 31st International Ludwig Wittgenstein-Symposium. Ontos, 63-78.
J. Glimm, D. Sharp, Stochastic Differential Equations: Selected Applications in Continuum Physics, in: R.A. Carmona, B. Rozovskii (ed.) Stochastic Partial Differential Equations: Six Perspectives, American Mathematical Society (October 1998) (ISBN 0-8218-0806-0).
wiki said:Many mathematical models of physical systems are deterministic. This is true of most models involving differential equations (notably, those measuring rate of change over time). Mathematical models that are not deterministic because they involve randomness are called stochastic. Because of sensitive dependence on initial conditions, some deterministic models may appear to behave non-deterministically; in such cases, a deterministic interpretation of the model may not be useful due to numerical instability and a finite amount of precision in measurement. Such considerations can motivate the consideration of a stochastic model even though the underlying system is governed by deterministic equations.
Wiki's references (appealing to authorities of philosophy and math):
Werndl, Charlotte (2009). Are Deterministic Descriptions and Indeterministic Descriptions Observationally Equivalent?. Studies in History and Philosophy of Modern Physics 40, 232-242.
Werndl, Charlotte (2009). Deterministic Versus Indeterministic Descriptions: Not That Different After All?. In: A. Hieke and H. Leitgeb (eds), Reduction, Abstraction, Analysis, Proceedings of the 31st International Ludwig Wittgenstein-Symposium. Ontos, 63-78.
J. Glimm, D. Sharp, Stochastic Differential Equations: Selected Applications in Continuum Physics, in: R.A. Carmona, B. Rozovskii (ed.) Stochastic Partial Differential Equations: Six Perspectives, American Mathematical Society (October 1998) (ISBN 0-8218-0806-0).