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Probability Theory III: Stochastic Calculus: Encyclopaedia of Mathematical Sciences, cartea 45

Editat de Yurij V. Prokhorov Traducere de P.B. Slater Contribuţii de S.V. Anulova Editat de Albert N. Shiryaev Contribuţii de N. V. Krylov, R.S. Liptser, A. N. Shiryaev, A.Yu. Veretennikov
en Limba Engleză Hardback – 25 noi 1997
Preface In the axioms of probability theory proposed by Kolmogorov the basic "probabilistic" object is the concept of a probability model or probability space. This is a triple (n, F, P), where n is the space of elementary events or outcomes, F is a a-algebra of subsets of n announced by the events and P is a probability measure or a probability on the measure space (n, F). This generally accepted system of axioms of probability theory proved to be so successful that, apart from its simplicity, it enabled one to embrace the classical branches of probability theory and, at the same time, it paved the way for the development of new chapters in it, in particular, the theory of random (or stochastic) processes. In the theory of random processes, various classes of processes have been studied in depth. Theories of processes with independent increments, Markov processes, stationary processes, among others, have been constructed. In the formation and development of the theory of random processes, a significant event was the realization that the construction of a "general theory of ran­ dom processes" requires the introduction of a flow of a-algebras (a filtration) F = (Ftk::o supplementing the triple (n, F, P), where F is interpreted as t the collection of events from F observable up to time t.
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Specificații

ISBN-13: 9783540546870
ISBN-10: 3540546871
Pagini: 253
Ilustrații: VI, 256 p.
Dimensiuni: 155 x 235 x 14 mm
Greutate: 0.55 kg
Ediția:1998
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Encyclopaedia of Mathematical Sciences

Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

1. Introduction to Stochastic Calculus.- 2. Stochastic Differential and Evolution Equations.- 3. Stochastic Calculus on Filtered Probability Spaces.- 4. Martingales and Limit Theorems for Stochastic Processes.- Author Index.