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Probability Theory I - Andrea Pascucci

Probability Theory I

Random Variables and Distributions

(Autor)

Buch | Softcover
XXI, 382 Seiten
2024
Springer International Publishing (Verlag)
978-3-031-63189-4 (ISBN)
CHF 82,35 inkl. MwSt
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This book provides a concise yet rigorous introduction to probability theory. Among the possible approaches to the subject, the most modern approach based on measure theory has been chosen: although it requires a higher degree of mathematical abstraction and sophistication, it is essential to provide the foundations for the study of more advanced topics such as stochastic processes, stochastic differential calculus and statistical inference. The text originated from the teaching experience in probability and applied mathematics courses within the mathematics degree program at the University of Bologna; it is suitable for second- or third-year students in mathematics, physics, or other natural sciences, assuming multidimensional differential and integral calculus as a prerequisite. The four chapters cover the following topics: measures and probability spaces; random variables; sequences of random variables and limit theorems; and expectation and conditional distribution. The text includes a collection of solved exercises.

Andrea Pascucci is a professor of Probability and Mathematical Statistics at the Alma Mater Studiorum - University of Bologna. His research activity encompasses various aspects of the theory of stochastic differential equations for diffusions and jump processes, degenerate partial differential equations, and their applications to mathematical finance. He has authored 6 books and over 80 scientific articles on the following topics: linear and nonlinear Kolmogorov-Fokker-Planck equations; regularity and asymptotic estimates of transition densities for multidimensional diffusions and jump processes; free boundary problems, optimal stopping, and applications to American-style financial derivatives; Asian options and volatility models. He has been invited as a speaker at more than 40 international conferences. He serves as an editor for the Journal of Computational Finance and is the director of a postgraduate program in Mathematical Finance at the University of Bologna.

1 Measures and probability spaces.- 2 Random variables.- 3 Sequences of random variables.- 4 Conditional probability.- 5 Summary exercises.- Appendix A: Dynkin's theorems.- Appencix B: Absolute continuity.- Appendix C: Uniform integrability.

Erscheinungsdatum
Reihe/Serie La Matematica per il 3+2
UNITEXT
Zusatzinfo XXI, 382 p. 24 illus., 16 illus. in color.
Verlagsort Cham
Sprache englisch
Original-Titel Teoria della Probabilità. Variabili aleatorie e distribuzioni
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte Conditional probability • Convergence of random variables • law of large numbers • Monte Carlo methods • Probability Distribution • Probability space • random variables
ISBN-10 3-031-63189-7 / 3031631897
ISBN-13 978-3-031-63189-4 / 9783031631894
Zustand Neuware
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