Continuous exponential martingales and BMO / Norihiko Kazamaki.

By: Kazamaki, Norihiko, 1940-
Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag): 1579.Publisher: Berlin ; New York : Springer-Verlag, ©1994Description: 1 online resource (vi, 90 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9783540484219; 3540484213Subject(s): Martingales (Mathematics) | Semi-martingales (Mathématiques) | Martingales (Mathematics) | Stochastische processen | Martingalen | Martingaltheorie | Martingal | Funktion beschränkter mittlerer OszillationGenre/Form: Electronic books. Additional physical formats: Print version:: Continuous exponential martingales and BMO.DDC classification: 510 s | 519.2/87 LOC classification: QA3 | .L28 no. 1579 | QA274.5Other classification: 31.70 | 31.00 Online resources: Click here to access online
Contents:
1. Exponential Martingales. 1.1. Preliminaries. 1.2. The L[rho]-integrability of [epsilon](M). 1.3. Girsanov's formula. 1.4. Uniform integrability of [epsilon](M) -- 2. BMO-Martingales. 2.1. The class BMO. 2.2. The John-Nirenberg inequality. 2.3. Characterizations of a BMO-martingale. 2.4. Fefferman's inequality. 2.5. The Garnett-Jones theorem. 2.6. The class [Eta infinite] -- 3. Exponential of BMO. 3.1. The reverse Holder inequality. 3.2. Gehring's inequality. 3.3. Transformation of BMO by a change of law. 3.4. A characterization of the BMO-closure of L[infinite]. 3.5. The class [Eta infinite] and the [Alpha subscript rho] condition. 3.6. Weighted norm inequalities. 3.7. Some ratio inequalities.
Action note: digitized 2010 committed to preserveSummary: In three chapters on Exponential Martingales, BMO-martingales, and Exponential of BMO, this book explains in detail the beautiful properties of continuous exponential martingales that play an essential role in various questions concerning the absolute continuity of probability laws of stochastic processes. The second and principal aim is to provide a full report on the exciting results on BMO in the theory of exponential martingales. The reader is assumed to be familiar with the general theory of continuous martingales.
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Includes bibliographical references (pages 85-90) and index.

In three chapters on Exponential Martingales, BMO-martingales, and Exponential of BMO, this book explains in detail the beautiful properties of continuous exponential martingales that play an essential role in various questions concerning the absolute continuity of probability laws of stochastic processes. The second and principal aim is to provide a full report on the exciting results on BMO in the theory of exponential martingales. The reader is assumed to be familiar with the general theory of continuous martingales.

1. Exponential Martingales. 1.1. Preliminaries. 1.2. The L[rho]-integrability of [epsilon](M). 1.3. Girsanov's formula. 1.4. Uniform integrability of [epsilon](M) -- 2. BMO-Martingales. 2.1. The class BMO. 2.2. The John-Nirenberg inequality. 2.3. Characterizations of a BMO-martingale. 2.4. Fefferman's inequality. 2.5. The Garnett-Jones theorem. 2.6. The class [Eta infinite] -- 3. Exponential of BMO. 3.1. The reverse Holder inequality. 3.2. Gehring's inequality. 3.3. Transformation of BMO by a change of law. 3.4. A characterization of the BMO-closure of L[infinite]. 3.5. The class [Eta infinite] and the [Alpha subscript rho] condition. 3.6. Weighted norm inequalities. 3.7. Some ratio inequalities.

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