The purpose of this note is to identify an interesting and surprising duality between the equations governing the probability distribution and expected value functional of the stochastic process deΓΏned by At := t 0 exp{Zs} ds; t ΒΏ 0; where {Zs: s ΒΏ 0} is a one-dimensional Brownian motion with drift
On positive and negative moments of the integral of geometric Brownian motions
β Scribed by Catherine Donati-Martin; Hiroyuki Matsumoto; Marc Yor
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 94 KB
- Volume
- 49
- Category
- Article
- ISSN
- 0167-7152
No coin nor oath required. For personal study only.
β¦ Synopsis
We present explicit formulae for the positive and negative moments of an exponential Wiener functional, which is deΓΏned as the integral with respect to time of geometric Brownian motion and plays an important role in several ΓΏelds.
π SIMILAR VOLUMES
We study the possibility to control the moments of Wiener integrals of fractional Brownian motion with respect to the L p -norm of the integrand. It turns out that when the self-similarity index H ΒΏ 1 2 , we can have only an upper inequality, and when H Β‘ 1 2 we can have only a lower inequality.
THE LINEARIZED EQUATIONS OF MOTION \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 3 MOBILITIES \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_.\_\_\_\_\_.\_.\_\_\_\_\_.\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 5 A\_ Lowest order multipole; point force approximation \_\_\_\_\_\_\_\_.\