## Large Deviations |

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### Common terms and phrases

0}-invariant AM(A apply assertion assume BANACH space Cb(fi;R CC E choose Clearly complete the proof conclude convergence convex function convex rate function CRAMER'S Theorem define denote DONSKER easy element of Mf ergodic Exercise exists exponentially tight fact FELLER continuous Finally full large deviation given governs the large grad Hence holds hypermixing JENSEN'S inequality l,oo large deviation principle large deviation theory LEGENDRE transform Lemma lime log lower semi-continuous MARKOV chain MARKOV family MARKOV property metric space Mf(fi Mi(E Mi(fi Mi(S Moreover non-decreasing notation P-almost particular Polish space preceding principle with rate probability measures prove random variables rate function right hand side satisfies the full SCHILDER'S Theorem semigroup sequence shift-invariant SKOROKHOD strong topology suppose transition probability function uniformly unique upper bound weak topology

### Popular passages

Page 1 - That is, one wants to know the rate at which /.t,.(ŁA) is tending to 0. In general, a detailed answer to this question is seldom available in the infinite dimensional setting. However, if one only asks about the exponential rate, the rate at which...

Page 1 - ... say that we omitted a great deal of small ball problems for other important processes such as Markov processes (in particular stable processes, diffusions with scaling), polygonal processes from partial sums, etc. Probably the most general formulation of small ball problems is the following. Let...