Brownian Motion: An Introduction To Stochastic Processes 2nd Edition by René L. Schilling (PDF)

Description

Brownian motion is one of the most important stochastic processes in continuous time and with continuous state space. Within the realm of stochastic processes, Brownian motion is at the intersection of Gaussian processes, martingales, Markov processes, diffusions and random fractals, and it has influenced the study of these topics. Its central position within mathematics is matched by numerous applications in science, engineering and mathematical finance. Often textbooks on probability theory cover, if at all, Brownian motion only briefly. On the other hand, there is a considerable gap to more specialized texts on Brownian motion which is not so easy to overcome for the novice. The authors’ aim was to write a book which can be used as an introduction to Brownian motion and stochastic calculus, and as a first course in continuous-time and continuous-state Markov processes. They also wanted to have a text which would be both a readily accessible mathematical back-up for contemporary applications (such as mathematical finance) and a foundation to get easy access to advanced monographs. This textbook, tailored to the needs of graduate and advanced undergraduate students, covers Brownian motion, starting from its elementary properties, certain distributional aspects, path properties, and leading to stochastic calculus based on Brownian motion. It also includes numerical recipes for the simulation of Brownian motion.

User’s Reviews

Editorial Reviews: About the Author René L. Schilling and Lothar Partzsch, Dresden University of Technology, Germany.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Really good book. Starts at the basics and explains everything very well. Kudos!

⭐The content is great. Unfortunately, the book is missing pages 22, 29, and 30. I returned the book for this reason, and Amazon sent me a different copy. This second copy was missing the same pages. If it were not missing these pages, I would rate it 5 stars. The material is well presented and easy to understand.

⭐Very clear. Detailed proofs and helpful comments. Offers beginners entry to a difficult subject. Guide to further reading is also very good.

⭐This book develops many important concepts in the study of stochastic processes in the context of the simple Brownian Motion process. I find it extremely well-written.

⭐Good for self study. The book has solutions on the author’s website. Though it requires measure theory and good grip on probability theory.

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