ENGLISH

Probability Theory II - Stochastic Calculus

By Andrea Pascucci

Book information

Publisher
Springer Nature Switzerland
Year
2024
ISBN
9783031631924, 9783031631931
DOI
10.1007/978-3-031-63193-1
ISSN
2532-3318
Language
english
Format
PDF
Filesize
13 MB (13639829 bytes)
Series
UNITEXT 166
Edition
1
Pages
426\428
Orientation
yes
Paginated
yes
Scanned
portrait
Time added
2024-09-04 12:11:17
Brownian MotionFeynman-Kac FormulasIto IntegralMarkov ProcessMartingaleStochastic differential equations

Description

This book offers a modern approach to the theory of continuous-time stochastic processes and stochastic calculus. The content is treated rigorously, comprehensively, and independently. In the first part, the theory of Markov processes and martingales is introduced, with a focus on Brownian motion and the Poisson process. Subsequently, the theory of stochastic integration for continuous semimartingales was developed. A substantial portion is dedicated to stochastic differential equations, the main results of solvability and uniqueness in weak and strong sense, linear stochastic equations, and their relation to deterministic partial differential equations. Each chapter is accompanied by numerous examples. This text stems from over twenty years of teaching experience in stochastic processes and calculus within master's degrees in mathematics, quantitative finance, and postgraduate courses in mathematics for applications and mathematical finance at the University of Bologna. The book provides material for at least two semester-long courses in scientific studies (Mathematics, Physics, Engineering, Statistics, Economics, etc.) and aims to provide a solid background for those interested in the development of stochastic calculus theory and its applications.

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