TY  - BOOK
AU  - Schilling,René L.
AU  - Böttcher,Björn
TI  - Brownian Motion: A Guide to Random Processes and Stochastic Calculus 
T2  - De Gruyter Textbook
SN  - 9783110741254
AV  - QA274.75 .S35 2021
U1  - 519.2/33 23
PY  - 2021///]
CY  - Berlin, Boston : 
PB  - De Gruyter, 
KW  - Brownian motion processes
KW  - Stochastic processes
KW  - Brownsche Bewegung
KW  - Finanzmathematik
KW  - Pfadeigenschaften
KW  - Stochastische Prozesse
KW  - MATHEMATICS / Probability & Statistics / General
KW  - bisacsh
N1  - Frontmatter --; Preface --; Contents --; Dependence chart --; 1 Robert Brown’s new thing --; 2 Brownian motion as a Gaussian process --; 3 Constructions of Brownian motion --; 4 The canonical model --; 5 Brownian motion as a martingale --; 6 Brownian motion as a Markov process --; 7 Brownian motion and transition semigroups --; 8 The PDE connection --; 9 The variation of Brownian paths --; 10 Regularity of Brownian paths --; 11 Brownian motion as a random fractal --; 12 The growth of Brownian paths --; 13 Strassen’s functional law of the iterated logarithm --; 14 Skorokhod representation --; 15 Stochastic integrals: L2-Theory --; 16 Stochastic integrals: localization --; 17 Stochastic integrals: martingale drivers --; 18 Itô’s formula --; 19 Applications of Itô’s formula --; 20 Wiener Chaos and iterated Wiener–Itô integrals --; 21 Stochastic differential equations --; 22 Stratonovich’s stochastic calculus --; 23 On diffusions --; 24 Simulation of Brownian motion by Björn Böttcher --; A Appendix --; Bibliography --; Index; restricted access; Issued also in print
N2  - Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''
UR  - https://doi.org/10.1515/9783110741278
UR  - https://www.degruyter.com/isbn/9783110741278
UR  - https://www.degruyter.com/document/cover/isbn/9783110741278/original
ER  -