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2000 Mathematics Subject Classification: 62P30.In this paper by using theory of large deviation techniques (LDT), the problem of hypotheses testing for three random variables having different distributions from three possible distributions is solved. Hypotheses identification for two objects having different distributions from two given probability distributions was examined by Ahlswewde and Haroutunian. We noticed Sanov's theorem and its applications in hypotheses testing.

On the distribution density of the supremum of a random walk in the subexponential case.

Korshunov, D.A. (2006)

Sibirskij Matematicheskij Zhurnal

On the distribution of random walk local time

A. N. Borodin (1987)

Annales de l'I.H.P. Probabilités et statistiques

On the large deviations of a class of modulated additive processes

Ken R. Duffy, Claudio Macci, Giovanni Luca Torrisi (2011)

ESAIM: Probability and Statistics

We prove that the large deviation principle holds for a class of processes inspired by semi-Markov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that the order in which elements in the set, called states, are visited is selected stochastically. The sojourn...

On the large deviations of a class of modulated additive processes

Ken R. Duffy, Claudio Macci, Giovanni Luca Torrisi (2012)

ESAIM: Probability and Statistics

On the left tail asymptotics for the limit law of supercritical Galton–Watson processes in the Böttcher case

Klaus Fleischmann, Vitali Wachtel (2009)

Annales de l'I.H.P. Probabilités et statistiques

Under a well-known scaling, supercritical Galton–Watson processes Z converge to a non-degenerate non-negative random limit variable W. We are dealing with the left tail (i.e. close to the origin) asymptotics of its law. In the Böttcher case (i.e. if always at least two offspring are born), we describe the precise asymptotics exposing oscillations (Theorem 1). Under a reasonable additional assumption, the oscillations disappear (Corollary 2). Also in the Böttcher case, we improve a recent lower deviation...

On the limit distribution of the well-distribution measure of random binary sequences

Christoph Aistleitner (2013)

Journal de Théorie des Nombres de Bordeaux

We prove the existence of a limit distribution of the normalized well-distribution measure $W (E_{N}) / \sqrt{N}$ (as $N \to \infty$ ) for random binary sequences $E_{N}$ , by this means solving a problem posed by Alon, Kohayakawa, Mauduit, Moreira and Rödl.

On the small deviation problem for some iterated processes.

Aurzada, Frank, Lifshits, Mikhail (2009)

Electronic Journal of Probability [electronic only]

On the small time asymptotics of the two-dimensional stochastic Navier–Stokes equations

Tiange Xu, Tusheng Zhang (2009)

Annales de l'I.H.P. Probabilités et statistiques

In this paper, we establish a small time large deviation principle (small time asymptotics) for the two-dimensional stochastic Navier–Stokes equations driven by multiplicative noise, which not only involves the study of the small noise, but also the investigation of the effect of the small, but highly nonlinear, unbounded drifts.

On Valiron and Circle Convergence.

Nicholas H. Bingham (1984)

Mathematische Zeitschrift

One-dimensional random field Kac's model: weak large deviations principle.

Picco, Pierre, Orlandi, Enza (2009)

Electronic Journal of Probability [electronic only]

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