Large deviation theorems for extended random variables and some applications

Hypotheses Testing in Nonergodic Fractional Ornstein-Uhlenbeck Models

“…The following assertion is a large deviation theorem of Chernoff type for the log-likelihood ratio process Λ T . The assertion was proved by means of large deviations theorems for extended random variables, see Linkov (1999).…”

Hypothesis testing for stochastic PDEs driven by additive noise

“…Obviously, if P(−∞ < S t < ∞) = 1, then m t (0) = 1. The following theorem is a Chernoff theorem for extended random variable S t under condition (m) with ǫ − < 0 < ǫ + (for details see for instance Lin ′ kov [16]).…”

On large deviations in testing Ornstein–Uhlenbeck-type models

“…In the rest of the section we refer some results about the asymptotic behavior of the error probabilities for Neyman-Pearson, Bayes, and minimax tests. The proofs of these results can be found in [22] (see also references in [23]). …”

“…Generalizations of the large deviation results to the case of semimartingale models and their applications are collected in the monograph [21]. Lin'kov [22] proved large deviation theorems for extended random variables and applied them to the investigation of general statistical experiments. Exact large deviation rates for the log-likelihood ratio in testing models with fractional Brownian motion were derived in [23].…”