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On Special Case of Multiple Hypotheses Optimal Testing for Three Differently Distributed Random Variables

Navaei, Leader (2011)

Serdica Mathematical Journal

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 spectral bandwidth of a stationary random process

Vladimír Klega (1983)

Aplikace matematiky

The irregularity coefficient is one of the numerical characteristics of the spectral bandwith of a stationary random process. Its basic properties are investigated and the application to the dichotomic classification of a process into narrow-band and wide-band ones is given. Further, its behaviour is analyzed for sufficiently wide classes of stationary processes whose spectral densities frequently appear both in theory and applications.

On stochastic differential equations with locally unbounded drift

István Gyöngy, Teresa Martínez (2001)

Czechoslovak Mathematical Journal

We study the regularizing effect of the noise on differential equations with irregular coefficients. We present existence and uniqueness theorems for stochastic differential equations with locally unbounded drift.

On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains

Weronika Łaukajtys (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

Let D be an open convex set in ℝ d and let F be a Lipschitz operator defined on the space of adapted càdlàg processes. We show that for any adapted process H and any semimartingale Z there exists a unique strong solution of the following stochastic differential equation (SDE) with reflection on the boundary of D: X t = H t + ∫ 0 t ⟨ F ( X ) s - , d Z s ⟩ + K t , t ∈ ℝ⁺. Our proofs are based on new a priori estimates for solutions of the deterministic Skorokhod problem.

On strong laws for generalized L-statistics with dependent data

David Gilat, Roelof Helmers (1997)

Commentationes Mathematicae Universitatis Carolinae

It is pointed out that a strong law of large numbers for L-statistics established by van Zwet (1980) for i.i.d. sequences, remains valid for stationary ergodic data. When the underlying process is weakly Bernoulli, the result extends even to generalized L-statistics considered in Helmers et al. (1988).

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