Abstract
Let X be a uniformly integrable, cadlag non-negative regular supermartingale. Such a process X has the representation
where At is continuous and increasing on the half open interval [0,∞), Ao = 0 and A may assign mass to ∞ which is just A∞+ - A∞ where \( {{\text{A}}_{\infty }} = \mathop{{\lim }}\limits_{{{\text{t}} \uparrow \infty }} {{\text{A}}_t} \). Then we have the maximal inequality.
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References
C. Dellacherie and P.A. Meyer, Probabilités et Potentiel, Chapitres V a VIII, Hermann, Paris, (1980).
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© 1989 Birkhäuser Boston
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Rao, K.M. (1989). A Maximal Inequality. In: Çinlar, E., Chung, K.L., Getoor, R.K., Glover, J. (eds) Seminar on Stochastic Processes, 1988. Progress in Probability, vol 17. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3698-6_14
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DOI: https://doi.org/10.1007/978-1-4612-3698-6_14
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