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Let a finite alphabet Ω. We consider a sequence of letters from Ω generated by a discrete time semi-Markov process ${Z_{γ}; γ \in} .$ We derive the probability of a word occurrence in the sequence. We also obtain results for the mean and variance of the number of overlapping occurrences of a word in a finite discrete time semi-Markov sequence of letters under certain conditions.

On the probability that integers chosen according to the binomial distribution are relative prime

J. Nymann, W. Leahey (1976)

Acta Arithmetica

On the product and ratio of Bessel random variables.

Nadarajah, Saralees, Gupta, Arjun K. (2005)

International Journal of Mathematics and Mathematical Sciences

On the product and ratio of Laplace and Bessel random variables.

Nadarajah, Saralees (2005)

Journal of Applied Mathematics

On the properties of the Generalized Normal Distribution

Thomas L. Toulias, Christos P. Kitsos (2014)

Discussiones Mathematicae Probability and Statistics

The target of this paper is to provide a critical review and to enlarge the theory related to the Generalized Normal Distributions (GND). This three term (position, scale shape) distribution is based in a strong theoretical background due to Logarithm Sobolev Inequalities. Moreover, the GND is the appropriate one to support the Generalized entropy type Fisher's information measure.

On the quadratic Wiener functional associated with the Malliavin derivative of the square norm of Brownian sample path on interval.

Taniguchi, Setsuo (2006)

Electronic Communications in Probability [electronic only]

On the ratio of Pearson type VII and Bessel random variables.

Nadarajah, Saralees, Kotz, Samuel (2005)

Journal of Applied Mathematics and Decision Sciences

On the relationship between Menger spaces and Wald spaces

Jack B. Brown (1973)

Colloquium Mathematicae

On the robustness of properties characterizing the normal distribution

Boguslawa Bednarek-Kozek, A. Kozek (1972)

Applicationes Mathematicae

On the spectrum of a distribution function and on unique factorization.

Pham-Gia, T. (1982)

International Journal of Mathematics and Mathematical Sciences

On the Support of the Measures in a Symmetric Convolution Semigroup.

Christian Berg (1976)

Mathematische Zeitschrift

On the supports and absolute continuity of infinitely divisible probability measures.

J. Yuan, T. C. Liang (1976)

Semigroup forum

On the tails of the distribution of the maximum of a smooth stationary gaussian process

Jean-Marc Azaïs, Jean-Marc Bardet, Mario Wschebor (2002)

ESAIM: Probability and Statistics

We study the tails of the distribution of the maximum of a stationary gaussian process on a bounded interval of the real line. Under regularity conditions including the existence of the spectral moment of order 8, we give an additional term for this asymptotics. This widens the application of an expansion given originally by Piterbarg [11] for a sufficiently small interval.

On the tails of the distribution of the maximum of a smooth stationary Gaussian process

Jean-Marc Azaïs, Jean-Marc Bardet, Mario Wschebor (2010)

ESAIM: Probability and Statistics

We study the tails of the distribution of the maximum of a stationary Gaussian process on a bounded interval of the real line. Under regularity conditions including the existence of the spectral moment of order 8, we give an additional term for this asymptotics. This widens the application of an expansion given originally by Piterbarg [CITE] for a sufficiently small interval.

On the Unimodality of Discrete Probability Measures.

Radu Theodorescu, Emile Bertin (1989)

Mathematische Zeitschrift

On the Urysohn condition and the convergence of probability distributions

Andrzej Kamiński (1988)

Czechoslovak Mathematical Journal

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