A Functional Interpretation of Cycloid Processes: Application to the Study of Asymptotic Behaviour |
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Authors: | S Kalpazidou L Tzouvaras |
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Institution: | (1) Department of Mathematics, Aristotle University, 54 006 Thessaloniki, Greece;(2) Polytechnic, Aristotle University, 54 006 Thessaloniki, Greece |
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Abstract: | We show that the classic Chapman–Kolmogorov equations of certain Markovian transition semigroups on finite state spaces have a formal analogy, of a homologic nature, in terms of cycloids
1, ...,
B, and positive numbers w1, ..., wB. The collection
k
,w
k
completely determines a Markov process {n}, called a cycloid process, admitting an invariant probability distribution, and decomposes its distribution Prob(n = , n + 1 = ) into a linear expression. The latter is further used in the study of the asymptotic behaviour of the cycloid process. |
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Keywords: | cycloid representations of Markov processes |
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