Probability Theory II : Stochastic Calculus / by Andrea Pascucci.

Format:

Book

Author/Creator:

Pascucci, Andrea.

Series:

La Matematica per il 3+2, 2038-5757 ; 166

Language:

English

Subjects (All):

Probabilities.

Social sciences--Mathematics.

Social sciences.

Probability Theory.

Mathematics in Business, Economics and Finance.

Local Subjects:

Probability Theory.

Mathematics in Business, Economics and Finance.

Physical Description:

1 online resource (428 pages)

Edition:

1st ed. 2024.

Place of Publication:

Cham : Springer Nature Switzerland : Imprint: Springer, 2024.

Summary:

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.

Contents:

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.

ISBN:

9783031631931

3031631935

OCLC:

1455132833