ادغام تصادفی (احتمال و آمار ریاضی)

Probability and Mathematical Statistics: A Series of Monographs and Textbooks: Stochastic Integration focuses on the processes, methodologies, and approaches involved in stochastic integration. The publication first takes a look at the Ito formula, stochastic integral equations, and martingales and semimartingales. Discussions focus on Meyer process and decomposition theorem, inequalities, examples of stochastic differential equations, general stochastic integral equations, and applications of the Ito formula. The text then elaborates on stochastic measures, including stochastic measures and related integration and the Riesz representation theorem. The manuscript tackles the special features of infinite dimensional stochastic integration, as well as the isometric integral of a Hubert-valued square integrable martingale, cylindrical processes, and stochastic integral with respect to 2-cylindrical martingales with finite quadratic variation. The book is a valuable reference for mathematicians and researchers interested in stochastic integration. Content: PROBABILITY AND MATHEMATICAL STATISTICS: A Series of Monographs and Textbooks, Page ii Front Matter, Page iii Copyright, Page iv PREFACE, Pages vii-ix ACKNOWLEDGMENTS, Page x NOTATION, Pages xi-xii CHAPTER 1 - STOCHASTIC INTEGRAL WITH RESPECT TO π-PROCESSES, Pages 1-34 CHAPTER 2 - THE ITO FORMULA, Pages 35-62 CHAPTER 3 - STOCHASTIC INTEGRAL EQUATIONS, Pages 63-92 CHAPTER 4 - MARTINGALES AND SEMIMARTINGALES, Pages 93-145 CHAPTER 5 - STOCHASTIC MEASURES, Pages 146-161 CHAPTER 6 - SPECIAL FEATURES OF INFINITE-DIMENSIONAL STOCHASTIC INTEGRATION, Pages 162-187 BIBLIOGRAPHY, Pages 188-194 INDEX, Pages 195-196 Stochastic Integral With Respect To [pi]-processes -- The Ito Formula -- Stochastic Integral Equations -- Martingales And Semimartingales -- Stochastic Measures -- Special Features Of Infinite-dimensional Stochastic Integration. Michel Métivier, J. Pellaumail. Includes Index. Bibliography: P. 188-194.