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Probability distribution solutions of a general linear equation of infinite order

Tomasz Kochanek, Janusz Morawiec (2009)

Annales Polonici Mathematici

Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We obtain a partial characterization and a uniqueness-type result for solutions of the general linear equation F ( x ) = Ω F ( τ ( x , ω ) ) P ( d ω ) in the class of probability distribution functions.

Probability distribution solutions of a general linear equation of infinite order, II

Tomasz Kochanek, Janusz Morawiec (2010)

Annales Polonici Mathematici

Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be a mapping strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We discuss the problem of existence of probability distribution solutions of the general linear equation F ( x ) = Ω F ( τ ( x , ω ) ) P ( d ω ) . We extend our uniqueness-type theorems obtained in Ann. Polon. Math. 95 (2009), 103-114.

Prolongement analytique et systèmes dynamiques discrets.

Augustin Fruchard (1992)

Collectanea Mathematica

We present a new method of analytic continuation of series out of their disk of convergence. We then exhibit a connection with the phenomenon of bifurcation delay in a planar discrete dynamical system; the limit of the method is then related to a stop phenomenon.

Properties of differences of meromorphic functions

Zong-Xuan Chen, Kwang Ho Shon (2011)

Czechoslovak Mathematical Journal

Let f be a transcendental meromorphic function. We propose a number of results concerning zeros and fixed points of the difference g ( z ) = f ( z + c ) - f ( z ) and the divided difference g ( z ) / f ( z ) .

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