03997nam a22005295i 4500 978-3-031-63193-1 DE-He213 20251030112934.0 cr nn 008mamaa 240903s2024 sz | s |||| 0|eng d 9783031631931 978-3-031-63193-1 10.1007/978-3-031-63193-1 doi QA273.A1-274.9 PBT bicssc PBWL bicssc MAT029000 bisacsh PBT thema PBWL thema Pascucci, Andrea. author. (orcid)0000-0001-8837-5568 https://orcid.org/0000-0001-8837-5568 aut http://id.loc.gov/vocabulary/relators/aut 77738 Probability Theory II [electronic resource] : Stochastic Calculus / by Andrea Pascucci. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIX, 426 p. 18 illus., 14 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda La Matematica per il 3+2, 2038-5757 ; 166 1 Stochastic processes -- 2 Markov processes -- 3 Continuous processes -- 4 Brownian motion -- 5 Poisson process -- 6 Stopping times -- 7 Strong Markov property -- 8 Continuous martingales -- 9 Theory of variation -- 10 Stochastic integral -- 11 Itô's formula -- 12 Multidimensional stochastic calculus -- 13 Change of measure and martingale representation -- 14 Stochastic differential equations -- 15 Feynman-Kac formulas -- 16 Linear stochastic equations -- 17 Strong solutions -- 18 Weak solutions -- 19 Complements.-20 A primer on parabolic PDEs. 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. This text completes the journey started with the first volume of Probability Theory I - Random Variables and Distributions, through a selection of advanced classic topics in stochastic analysis. Probabilities. 65724 Social sciences Mathematics. 69736 Probability Theory. 67428 Mathematics in Business, Economics and Finance. 69739 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031631924 Printed edition: 9783031631948 La Matematica per il 3+2, 2038-5757 ; 166 70145 https://doi.org/10.1007/978-3-031-63193-1 ZDB-2-SMA ZDB-2-SXMS 63053 63053