Download presentation

Presentation is loading. Please wait.

Published byHalle Montague Modified over 2 years ago

1
Vadym Omelchenko

2
Definition

3
Donsker Theorem

4
Proof

9
Proof of the tightness

10
Proof (Proof of the Lemma)

12
Hence both (A) and (B) imply (3) which is the affirmation of the theorem. QED

13
Proof

15
Having proved the assertion of this theorem for finite- dimensional distributions and having proved the tightness we have proved the theorem. QED

16
Application of Donsker Theorem

17
Unit Dimension {-1,+1} N=20 N=60 N=1000

18
Application of Donsker’s Theorem More important than this qualitative interpretation is the use of Donsker's theorem to prove limit theorems for various functions of the partial sums

19
Application of Donsker’s Theorem

20
Random Walk and Reflection Principle

21
Hence we have:

22
Combining the results (**) and (***) we have:

24
Functions of Brownian M. Paths

26
The Arc Sine Law

32
Example(1) Normal and Student-t

33
Example (2)

34
Brownian Bridge

Similar presentations

OK

13.4 Mathematical Induction. Mathematical Induction is a common method of proving that each statement of an infinite sequence of mathematical statements.

13.4 Mathematical Induction. Mathematical Induction is a common method of proving that each statement of an infinite sequence of mathematical statements.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on edge detection pdf Ppt on geography of india Ppt on blood stain pattern analysis jobs Ppt on eye os glasses Ppt on world water day 2013 Ppt on conservation of ocean resources Ppt on regional trade agreements and wto Ppt on p&g products free samples Ppt on teachers day poem Ppt on statistics in maths what does product