University COVID-19 update

The University of Waterloo is constantly updating our most Frequently Asked Questions.

Questions about buildings and services? Visit the list of Modified Services.

Please note: The University of Waterloo is closed for all events until further notice.

Department seminar by Yizo Wang, University of CincinnatiExport this event to calendar

Thursday, March 10, 2016 — 4:00 PM EST

 Limit theorems and long-range dependence

 It is a well known result that a simple random walk scales to a Brownian motion, after appropriate normalization. When the steps of random walk are no longer independent but only stationary, Brownian motions may still arise in the limit, if the dependence are weak enough. On the other hand, when the dependence are strong enough, different types of stochastic processes may arise in the limit, after normalizations at different orders. Such results provide important examples of the so-called long-range phenomena, extensively investigated in various areas including telecommunication, finance, hydrology and statistical physics, among others.

In the first half of this talk, we provide a brief overview of research along this line, and in particular highlight a few representative limit theorems where fractional Brownian motions arise in the limit. In the second half of the talk, we present limit theorems on a specific infinite urn scheme proposed by Karlin (1967). The Karlin model can be also viewed as a correlated random walk, and moreover our result shows that its decomposition can be understood as the discrete counterpart to the decomposition of fractional Brownian motions by bi-fractional Brownian motions recently revealed by Lei and Nualart (2009).
                        
Joint work with Olivier Durieu (Université François Rabelais de Tours, France).

Location 
M3 - Mathematics 3
3127

,
Canada

S M T W T F S
25
26
27
28
29
30
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
1
2
3
4
5
  1. 2021 (47)
    1. October (1)
    2. September (2)
    3. July (1)
    4. May (4)
    5. April (8)
    6. March (13)
    7. February (7)
    8. January (12)
  2. 2020 (71)
    1. December (2)
    2. November (13)
    3. October (16)
    4. September (7)
    5. August (5)
    6. July (3)
    7. June (2)
    8. May (1)
    9. March (4)
    10. February (4)
    11. January (14)
  3. 2019 (65)
  4. 2018 (44)
  5. 2017 (55)
  6. 2016 (44)
  7. 2015 (38)
  8. 2014 (44)
  9. 2013 (46)
  10. 2012 (44)