Displaying similar documents to “Doubly stochastic compound Poisson processes in extreme value theory.”

On the Diophantine equation x 2 - k x y + y 2 - 2 n = 0

Refik Keskin, Zafer Şiar, Olcay Karaatlı (2013)

Czechoslovak Mathematical Journal

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In this study, we determine when the Diophantine equation x 2 - k x y + y 2 - 2 n = 0 has an infinite number of positive integer solutions x and y for 0 ≤ n ≤ 10 . Moreover, we give all positive integer solutions of the same equation for 0 ≤ n ≤ 10 in terms of generalized Fibonacci sequence. Lastly, we formulate a conjecture related to the Diophantine equation x 2 - k x y + y 2 - 2 n = 0 .

Two mutually rarefied renewal processes

Ilona Kopocińska (1994)

Applicationes Mathematicae

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Let us consider two independent renewal processes generated by appropriate sequences of life times. We say that a renewal time is accepted if in the time between a signal and the preceding one, some signal of the second process occurs. Our purpose is to analyze the sequences of accepted renewals. For simplicity we consider continuous and discrete time separately. In the first case we mainly consider the renewal process rarefied by the Poisson process, in the second we analyze the process...