Excursions of Markov Processes - Rilegato

Blumenthal, Robert M.

Rilegato

ISBN 10: 0817635750 ISBN 13: 9780817635756

Casa editrice: Birkhauser, 1991

Riassunto

Let {Xti t ~ O} be a Markov process in Rl, and break up the path X t into (random) component pieces consisting of the zero set ({ tlX = O}) and t the "excursions away from 0," that is pieces of path X. : T ::5 s ::5 t, with Xr- = X = 0, but X. 1= 0 for T < s < t. When one measures the time in t the zero set appropriately (in terms of the local time) the excursions acquire a measure theoretic structure practically identical to that of processes with stationary independent increments, except the values of the process are paths rather than real numbers. And there is a measure on path space that helps describe the measure theoretic properties of the excursions in the same way that the Levy measure describes the jumps of a process with independent increments. The entire circle of ideas is called excursion theory. There are many attractive things about the subject: it is an area where one can use to advantage general probabilistic potential theory to make quite specific calculations, it provides a natural setting for apply­ ing esoteric things like David Williams' path decomposition, it provides a method for constructing processes whose description in terms of an in­ finitesimal generator or some such analytic object would be complicated. And the ideas seem to be closely related to a good deal of current research in probability.

Dettagli dell?edizione

• Editore: Birkhauser
• Data di pubblicazione: 1991
• ISBN 10: 0817635750
• ISBN 13: 9780817635756
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero edizione: 1
• Numero di pagine: 288