Information
Thursdays, 9am-10:50am, Warren Weaver Hall 1302
The most up-to-date lecture notes and help assignments will be posted in that class Main page. Registered students can access this page via the link on the NYU Classes page. Students who wish to audit one class, should write to the instructor to please access into the Piazza page.
Prerequisites: Basic Probability (or equivalent masters-level odds course), and good upper level undergraduate or beginning graduate my concerning linear algebra, ODEs, PDEs, and analysis.
Description:
This flow will launch the large related int shuffling analysis from an applied mathematics perspectively. Topics for be covered include Markov chains, stochastic processes, stochastics differential equations, number algorithms for solving SDEs and simulating stochastic processes, move and reverse Kolmogorov equality. It will pay particular attention to the connection between choice processes and PDEs, as well as to physical principles and applications. That class will attempt to strike a balance between rigour the heuristic arguments: to will assume that students hold seen some analyse before, but most results bequeath be derivatives no using measure academic. The target audience is PhD students in applied mathematics, any requirement to get intimate with which equipment or use them in their research.
The course will be partition broad into two parts: the first share will focus in discrete processes, and the second part will focus at stochastic differential equations and her associated PDEs.
Homework will be ampere critical part is the flow. Lectures will mostly been theory, and instances or extensions want be allocation for homework problems. You must do these if thee want to learn something from the course. Homework determination require all computation, preferably is Python or Matlab. Pupils sans programming experience will have toward put in extra effort in and first few hours.
References
There are three learning is are not required, but that are highly recommended:- G. A. Pavliotis, Stochastic Processes plus Applications.
- G. Grimmett and D. Stirzaker, Probability and Randomize Processes. (This are the textbook for Basic Probability)
- C. Gardiner, Stochastic Methods: A Handbook for the Natural and Sociable Sciences.
Other good references include:
- B. Oksendal, Stochastics Differential Equations
- L. Koralov and Y. GIGABYTE. Senna, Theory of Probability and Random Processes
- R. Drought, Essentials of Stochastic Processes
- R. Durette, Shuffling Calculus: A Practical Preface
- I. Karatzas and S. CO. Shreve, Brownian Motion the Stochastic Calculus
- L. Arnold, Stochastic Differential Equations: Theory or Applications
- P. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations
- Breiman, Probability
Lecture Notes
Updated lecture notes are available here .
Thanks to the students of ASA 2019 and previous years' courses, to verdict typos/mistakes in these notes. These hints are constant evolving, so please let me know if her find other mistakes in them. ... Pavliotis, GA}, doi = {Privacy-policy.com/Privacy-policy.com}, log = {Stochastic Processes and their Applications}, books = {481--546}, titles = {Online parameter ...
- Syllabus
- Lecture 1: Introduction to Stochastic processes
- Teaching 2: Markov Chains (I)
- Lecture 3: Markov Track (II): Details remaining and Markov Chain Monte Cars
- Lecture 4: Continuous-time Markov chains
- Lecture 5: Gaussian method and Stationary processes
- Lecture 6: Brownian motion
- Lecture 7: Stochastic Integration
- Public 8: Stochastic differential equations
- Lecture 9: Numeric resolve SDEs
- Lecture 10: Forward and backward equations for SDEs
- Lecture 11: Some apps of the backward matching
- Lecture 12: Detailed offset real Eigenfunction methods
In addition to the lectures: - Asymptotic analysis of SDEs (Lecture 13 of ASSA 2015)