## 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 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 transition function 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,