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A Large Deviation Approximation for Multivariate Density Functions
Mathematical Methods of Statistics, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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ON A SUFFICIENT CONDITION FOR LARGE DEVIATIONS OF ADDITIVE FUNCTIONALS
Stochastics and Dynamics, 2011We prove the large deviation principle for continuous additive functionals under certain assumptions. The underlying symmetric Markov processes include Brownian motion and symmetric and relativistic α-stable processes.
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Functional Approach of Large Deviations in General Spaces
Journal of Theoretical Probability, 2005Let \((\mu_{\alpha})\) be a net of Borel probability measures on a topological space \(X\), and \((t_{\alpha})\) a net in \(]0,{\infty}[\) converging to \(0\). For each \([-{\infty}, +{\infty}[\)-valued measurable function \(h\) on \(X\), we define \(\Lambda(h)=\log \lim (\int_X \exp{{h(x)}\over{t_\alpha}} \mu_{\alpha}(dx))^{t_\alpha}\) provided the ...
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Large deviations for functionals of stationary processes
Probability Theory and Related Fields, 1990Let \((S_ n)\) be a sequence of \(R^ d\)-valued random variables adapted to the internal history of a stationary sequence of random elements \((X_ n)\). We formulate conditions under which the principle of large deviations holds true for the sequence \((S_ n)\).
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Rényi Entropies and Large Deviations for the First Match Function
IEEE Transactions on Information Theory, 2015We define the first match function $T_{n}:{\mathcal C}^{n} \rightarrow \{1,\ldots ,n\}$ where ${\mathcal C}$ is a finite alphabet. For two copies of ${x}_{1}^{n} \in {\mathcal C} ^{n}$ , this function gives the minimum number of steps one has to slide one copy of ${x}_{1}^{n}$ to get a match with the other one.
Miguel Natalio Abadi, Liliam Cardeno
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Rate functions in the theory of large deviations
Statistics & Probability Letters, 1996Let \(X\) be a normal topological space and \((P_n)_n\) a sequence of probability measures on \(X\) which satisfies a large deviation principle on \(X\) with a rate function \(I\). \textit{I. H. Dinwoodie} [Ann. Probab. 21, No. 1, 216-231 (1993; Zbl 0777.60024)] has established that \(I\) can be represented as \[ I(x) = \sup \bigl\{ f(x) - \Phi (f),\;f
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Variational form of the large deviation functional
Statistics & Probability Letters, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A lemma on large deviations of arithmetic functions
Lithuanian Mathematical Journal, 1983Let \(f\) be an additive arithmetic function. Denote by \(A(x)=\sum_{p\leq x} f(p)p^{-1}\) and \(B(x)=\sum_{p\leq x}f^2(p)p^{-1},\) where \(p\) is prime. Suppose that \[ \mu_x=(\sup_{p\leq x}| f(p)|)/\sqrt{B(x)}\to 0\text{ as }x\to \infty. \] Then it is well known that as \(x\to \infty\), \[ F_x(v)=(1/x) \sum_{\substack{n\le x \\ f(n)- A(x)
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On Large Deviations for Additive Functionals of Markov Processes I
Theory of Probability & Its Applications, 1994Large deviations for Markov processes are investigated using the Wentzell-Freidlin-Gärtner method. The problem concerning deviations of sums of a component of a Markov process is considered for the case when it is impossible to apply directly the main theorem for positive operators, i.e., the Frobenius theorem on spectral radius.
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Large Deviations for Additive Functionals of Symmetric Stable Processes
Journal of Theoretical Probability, 2007zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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