Stochastic analysis 2020 2021 — различия между версиями

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(не показаны 52 промежуточные версии 2 участников)
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|| Lecturer || [https://www.hse.ru/staff/anaumov Naumov Alexey ] || [anaumov@hse.ru] || T924
 
|| Lecturer || [https://www.hse.ru/staff/anaumov Naumov Alexey ] || [anaumov@hse.ru] || T924
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|| Lecturer || [https://www.hse.ru/org/persons/93130881 Belomestny Denis ] || [dbelomestny@hse.ru] || T926
 
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|| Seminarist || [https://www.hse.ru/org/persons/219484540 Samsonov Sergey] || [svsamsonov@hse.ru] || T926
 
|| Seminarist || [https://www.hse.ru/org/persons/219484540 Samsonov Sergey] || [svsamsonov@hse.ru] || T926
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== About the course ==
 
== About the course ==
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This page contains materials for Stochastic Analysis course in 2020/2021 year, mandatory one for 1st year master students of Statistical Learning Theory program (HSE and Skoltech).
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This page contains materials for Stochastic Analysis course in 2020/2021 year, mandatory one for 1st year Master students of the Statistical Learning Theory program (HSE and Skoltech).
  
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== Grading formula ==  
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== Grading ==  
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The final grade consists of 4 components (each is non-negative real number from 0 to 10, without any intermediate rounding) :
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The final grade consists of 3 components (each is non-negative real number from 0 to 10, without any intermediate rounding) :
 
* O<sub>HW</sub> for the hometasks
 
* O<sub>HW</sub> for the hometasks
 
* O<sub>Mid-term</sub> for the midterm exam
 
* O<sub>Mid-term</sub> for the midterm exam
 
* O<sub>Exam</sub> for the final exam   
 
* O<sub>Exam</sub> for the final exam   
 
The formula for the final grade is  
 
The formula for the final grade is  
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* O<sub>Final</sub> = 0.3*O<sub>HW</sub> + 0.3*O<sub>Mid-term</sub> + 0.4*O<sub>Exam</sub>
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* O<sub>Final</sub> = 0.3*O<sub>HW</sub> + 0.3*O<sub>Mid-term</sub> + 0.4*O<sub>Exam</sub> + 0.1*O<sub>Bonus HW</sub>
 
with the usual (arithmetical) rounding rule.
 
with the usual (arithmetical) rounding rule.
  
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== Lectures ==
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[https://docs.google.com/spreadsheets/d/1MPWVIkgxyotHU-P5cE7Gik4C6RTWxTnAVK8Btl7Fw3Y/edit?usp=sharing '''Table with grades''']
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*[https://www.dropbox.com/s/6ycympj3ad44rns/Stochastic%20analysis%20lecture%20notes.pdf?dl=0 '''Lecture 05.09''']
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== Seminars ==
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== Lectures and Seminars ==
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*To be filled
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*[https://www.dropbox.com/s/a3im5ruldcdsoy7/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%201%20%282%29.pdf?dl=0 '''Lecture 05.09''']
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* [https://www.dropbox.com/s/4q3l1u6os9jtqml/Lecture_12_09.pdf?dl=0 '''Lecture 12.09''']
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* [https://www.dropbox.com/s/pjrtvkia3zu8tx6/Lecture_19_09.pdf?dl=0 '''Lecture 19.09''']
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* [https://www.dropbox.com/s/gqsttggpwiz7040/Seminar_19_09_stochan.pdf?dl=0 '''Seminar 19.09''']
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* [https://www.dropbox.com/s/3asrxd56bbljkii/Martingales.pdf?dl=0 '''Lecture-Seminar 26.09, part 1 (Martingales)''']
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* [https://www.dropbox.com/s/vqvzh7vb1cq96l7/Gaussian%20Process.pdf?dl=0 '''Lecture-Seminar 26.09, part 2 (Wiener process)''']
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* [https://www.dropbox.com/s/kpndh6fpnn8jpbe/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%203%20.pdf?dl=0 '''Lecture 03.10''']
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* [https://www.dropbox.com/s/pqhvmrupzbh6rs0/Seminar_03_10.pdf?dl=0 '''Seminar 03.10''']
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*[https://www.dropbox.com/s/18xv3jlbw5mfrnj/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%204%20%282%29.pdf?dl=0 '''Lecture 17.10''']
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*[https://www.dropbox.com/s/jgndwtup4v3jlgc/Seminar_30_10.pdf?dl=0 '''Seminar 31.10''']
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*[https://www.dropbox.com/s/9fd3l5vgw7g35jj/Copy%20of%20Stochastic%20analysis%20lecture%20notes.pdf?dl=0 Lectures on Markov chains]
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*[https://www.dropbox.com/s/psammzm24aji9cc/Seminar_14_11.pdf?dl=0 '''Seminar 14.11''']
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*[https://www.dropbox.com/s/5qdd7686oqzr5f7/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%207.pdf?dl=0 '''Lecture 21.11''']
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*[https://www.dropbox.com/s/pu6o0z6822g798d/Seminar_21_11.pdf?dl=0 '''Seminar 21.11''']
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*[https://www.dropbox.com/s/ps4gxwuhhq7blej/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%208.pdf?dl=0 '''Lecture 28.11''']
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*[https://www.dropbox.com/s/bt89nox8xb6tb25/Seminar_28_11.pdf?dl=0 '''Seminar 28.11''']
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*[https://www.dropbox.com/s/q20vaov6lm925oc/%D0%A1%D1%82%D0%BE%D1%85%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7_%20%D0%BB%D0%B5%D0%BA%D1%86%D0%B8%D1%8F%209.pdf?dl=0 '''Lecture 05.12''']
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*[https://www.dropbox.com/s/eic0xrko14quuqv/Seminar_12_12.pdf?dl=0 '''Seminar 12.12''']
  
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==Midterm ==
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==Homeworks ==
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*[https://www.dropbox.com/s/k1adzfss7hdg39z/HW_1_stochan_2020.pdf?dl=0 '''Homework №1, deadline: 10.10.2020, 23:59''']
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*[https://www.dropbox.com/s/pm9ffkzt66ax2lb/HW_2_stochan_2020.pdf?dl=0 '''Homework №2, deadline: 17.11.2020, 23:59''']
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*[https://www.dropbox.com/s/o58unavut1lu4a5/HW_3_stochan_2020.pdf?dl=0 '''Homework №3, deadline: 10.12.2020, 23:59''']
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*[https://www.dropbox.com/s/8drzo3o9z1pl3d8/HW_4_stochan_2020%20%281%29.pdf?dl=0 '''Homework №4 (bonus), deadline: 23.12.2020, 23:59''']
  
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==Exam==
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== Exam ==
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Exam will be held on 21.12.2019 at 10:30 in the following mixed form. First, you will have 1.5 hour to solve 4 problems. During this part you may use any resources (books, notes, laptops, etc). Then the oral part begins: you go to examinator with your solutions and answer some additional questions on the course. You are supposed to answer without preparation, so no proofs are needed. But you need to know the definitions, formulations of main results, and explain the key concepts. The final grade consists of the grade for the problems (20%) and for the oral answer (20%).
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*[https://us02web.zoom.us/j/86598258441?pwd=bUtMdHhwQmFmVUVzQkR0SjMrTTRIQT09 '''Conference link''']
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*[https://www.dropbox.com/s/omlg25jwzdptwav/Questions_stochan_final.pdf?dl=0 List of questions]
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*[https://www.dropbox.com/s/czer7y0jsgho7ir/Exam_stochan_2020.pdf?dl=0 '''Exam 23.12''']
  
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== Hometasks ==
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==Midterm ==
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*[https://www.dropbox.com/s/t8yhf64e784vdtw/hw_1_stochastic_analysis.pdf?dl=0 Homework №1], deadline - 12.10.2019, 23:59
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Midterm will take place on Saturday, 07.11.2020, at 11:10. You are allowed to use your lectures and seminar notes, or any other notes or books, but NOT the laptops, mobile phones and other devices. Midterm will take 1.5 hours and it will contain 6 problems. Solving any 5 of them will give you the maximal grade.  
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*[https://www.dropbox.com/s/kfsyssv45peev2n/HW_2_stochan.pdf?dl=0 Homework №2], deadline - 06.11.2019, 23:59
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*[https://www.dropbox.com/s/dwzwwuv6ed5i6lq/Questions_stochan_midterm.pdf?dl=0 '''List of topics''']
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*[https://www.dropbox.com/s/bk9e1pwdrq0rzyo/HW_3_stochan.pdf?dl=0 Homework №3], deadline - 01.12.2019, 23:59, [https://www.dropbox.com/s/nuktfsxiryztma3/File_with_hint_do_not_open_until_emergency.pdf?dl=0 Explicit recurrence for №4, do not open until emergency]
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*[https://www.dropbox.com/s/3yktcr8u7dyk1s7/HW_4_stochan%20%282%29.pdf?dl=0 Homework №4], deadline - 22.12.2019, 23:59
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<br><span style="color:#DC143C">Deadline postponed by 1 day</span>
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*[https://www.dropbox.com/s/gldo61bg4r29u4f/HW_bonus_stochan.pdf?dl=0 Bonus hometask], deadline - 22.12.2019, 23:59 [https://www.dropbox.com/s/x1oj4t0lq20ou7u/swiss.csv?dl=0 dataset]
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== Grades and results ==
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*[https://docs.google.com/spreadsheets/d/1ApuKS3flYKdhKiL_fVPCDnUumfOlrh9SYuZ79LRRpN4/edit?usp=sharing Results]
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== Recommended literature (1st term) ==
 
== Recommended literature (1st term) ==
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*https://link.springer.com/book/10.1007%2F978-3-319-62226-2 - Stochastic Calculus by P. Baldi, good overview of conditional probabilities and expectations (part 4, also accessible through HSE network)
 
*https://link.springer.com/book/10.1007%2F978-3-319-62226-2 - Stochastic Calculus by P. Baldi, good overview of conditional probabilities and expectations (part 4, also accessible through HSE network)
 
*https://link.springer.com/book/10.1007%2F978-1-4419-9634-3 - Probability for Statistics and Machine Learning by A. Dasgupta, chapter 19 (MCMC), also accessible through HSE network
 
*https://link.springer.com/book/10.1007%2F978-1-4419-9634-3 - Probability for Statistics and Machine Learning by A. Dasgupta, chapter 19 (MCMC), also accessible through HSE network
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== Recommended literature (2nd term) ==
 
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*https://link.springer.com/book/10.1007%2F978-1-4419-9634-3 - Probability for Statistics and Machine Learning by A. Dasgupta, chapter 12, 14
 
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*https://link.springer.com/book/10.1007/978-3-540-68829-7 - Probability theory and Random Processes by L. Koralov and Y. Sinai, lecture 13 (Conditional expectations and martingales)
 
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*https://link.springer.com/book/10.1007%2F978-3-319-62226-2 - Stochastic Calculus by P. Baldi - chapter 7,8 (Denis followed this book);
 
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*http://th.if.uj.edu.pl/~gudowska/dydaktyka/Oksendal.pdf - Stochastic Differential Equations by B. Oksendal (another exposition of the stochastic calculus) - chapters 3-5;
 
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==Additional reading (Lecture from 14.12 and related topics) ==
 
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*https://web.math.princeton.edu/~rvan/APC550.pdf- Ramon van Handel, Probability in High Dimension, chapter 2 (but I strongly recommend this book for your future course with Q. Paris, it is amazing);
 
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*https://www.springer.com/gp/book/9783319002262 - Gentil, Barky, Ledoux. Classical book on Markovian semigroups, not very easy to read;
 

Текущая версия на 11:18, 23 декабря 2020

Lecturers and Seminarists

Lecturer Naumov Alexey [anaumov@hse.ru] T924
Lecturer Belomestny Denis [dbelomestny@hse.ru] T926
Seminarist Samsonov Sergey [svsamsonov@hse.ru] T926

About the course

This page contains materials for Stochastic Analysis course in 2020/2021 year, mandatory one for 1st year Master students of the Statistical Learning Theory program (HSE and Skoltech).

Grading

The final grade consists of 3 components (each is non-negative real number from 0 to 10, without any intermediate rounding) :

  • OHW for the hometasks
  • OMid-term for the midterm exam
  • OExam for the final exam

The formula for the final grade is

  • OFinal = 0.3*OHW + 0.3*OMid-term + 0.4*OExam + 0.1*OBonus HW

with the usual (arithmetical) rounding rule.

Table with grades

Lectures and Seminars

Homeworks

Exam

Midterm

Midterm will take place on Saturday, 07.11.2020, at 11:10. You are allowed to use your lectures and seminar notes, or any other notes or books, but NOT the laptops, mobile phones and other devices. Midterm will take 1.5 hours and it will contain 6 problems. Solving any 5 of them will give you the maximal grade.

Recommended literature (1st term)

Источник — «http://wiki.cs.hse.ru/index.php?title=Stochastic_analysis_2020_2021&oldid=48954»