  It has often been observed that the Multifractal Formalism and the Large
Deviation Principles are intimately related. In fact, Multifractal Formalism
was heuristically derived using the Large Deviations ideas. In numerous
examples in which the multifractal results have been rigorously established,
the corresponding Large Deviation results are valid as well. Moreover, the
proofs of multifractal and large deviations are remarkably similar. The natural
question then is whether under which conditions multifractal formalism can be
deduced from the corresponding large deviations results. More specifically,
given a sequence of random variables $\{ {X_n} \}_{n\in\N}$, satisfying a Large
Deviation Principle, what can be said about the multifractal nature of the
level sets $K_\alpha=\{\omega: \lim_{n} \frac{X_n(\omega)}{n}=\alpha\}$. Under
some technical assumptions, we establish the upper and lower bounds for
multifractal spectra in terms of the large deviation rate functions, and show
that many known results of multifractal formalism are covered by our setup.
