It is an interesting exercise to compute the iterated integrals of
Brownian Motion and to calculate the expectations (of polynomial
functions of these integrals).

Recent work on constructing discrete measures on path space, which give
the same value as Wiener measure to certain of these expectations, has
led to promising new numerical algorithms for solving 2nd order
parabolic PDEs in moderate dimensions. Old work of Krylov associated
finitely additive signed measures to certain constant coefficient PDEs
of higher order. Recent work with Levin allows us to identify the
relevant expectations of iterated integrals in this case, leaving many
interesting open questions and possible numerical algorithms for solving
high dimensional elliptic PDEs.

Lecture #13337

Need help? Visit our help pages at http://www.msri.org/communications/vmath/hints

Streaming Video

This is a high quality streaming video encoded with MPEG-4 and with 640x480 resolution.

Windows and Mac users, QuickTime 6.5 or later required
Linux users, please see our Linux Help Page on how to view our streaming videos

Follow this link to --- Watch the Video Now Via Streaming Video ---

Download QuickTime File

You can download the QuickTime file here. Right click on the link and "Save As..." to save to your local computer.

• 13337-13337-QuickTime.mov (268 MB)

Create a DVD

You can download the video and audio files here. Please note that you need both files to create a DVD. Right click on the link and "Save As..." to save to your local computer. You can find instructions on how to create a DVD on our help page at http://www.msri.org/communications/vmath/author

• 13337-13337-DVD PCM Audio.aiff (572 MB - Audio Only)
• 13337-13337-MPEG-2 120min High Quality Encode.m2v (1302 MB - Video Only)

Buy the DVD

If none of the options work for you, you can always buy the DVD of this lecture.

If you would like to purchase a copy of this video for $15+shipping, please Click Here!

See more of our Streaming Videos on our main VMath - Streaming Video page.