## Essays on the Prediction Process |

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### Common terms and phrases

a-fields apply assertion assume autonomous germ-Markov Borel set Borel transition function Brownian motion complete Borel packet completing the proof conditional probabilities continuous local martingale corresponding countable define Dellacherie denote discontinuities Doob-Meyer decomposition EhM2 equivalent Essay finite follows Getoor given h e H H fl H hence Hft fl HQ implies initial distribution integrable martingales jumps l.ll left limits Levy system limsup Lusin space Markov process measurable functions metric space metrizable moderate Markov property notation null set obtain P-null set p(Zt potential prediction process prediction space previsible stopping probability space process Zt prove r.c.l.l. paths rational Ray process Ray topology relative to F REMARK right process right-continuous section theorem stochastic process Strasbourg subset supermartingale Theorem l.2 totally inaccessible uniformly integrable unique universally measurable weak convergence z e H Z^-previsible

### Popular passages

Page 56 - Sur la representation des martingales comme integrales stochastiques dans les processus ponctuels.

Page v - The shape of the hull has been kept as simple as possible, in order to make it easier for the amateur builder to underr take and complete.

Page 45 - Meyer, PA and Yor, M. Sur la theorie de la prediction, et le probleme de decomposition des tribus F?+ . Seminaire de Prob.

Page 56 - P. -A. and Yor, M. Sur la theorie de la prediction, et le probleme de decomposition des tribus F?+ . Seminaire de Prob. X, Univ. de Strasbourg, 104-117. Lecture Notes in Math. 511, Springer, Berlin, 1976. 13. Walsh, JB and Meyer, P. -A. "Quelques application des resolvantes de Ray," Inventiones Mathematicae, 14, 1971, 143-166.

Page 44 - Dynkin, EB Theory of Markov Processes. Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1961. 7. Engelbert, HJ "Markov processes in general state spaces

Page 85 - Levy systems, and most of the work needed for the proof has already been done in [2, Chapter 4, Section 3] and therefore need not be repeated here.

Page 67 - A predictive view of continuous time processes," Ann. Probability, 3, 1975, 573-596. 6. Knight, FB "Prediction processes and an autonomous germMarkov property,