Abstract
The conditional Feynman-Kac functional is used to derive the Laplace transforms of conditional maximum distributions of processes related to third- and fourth-order equations. These distributions are then obtained explicitly and are expressed in terms of stable laws and the fundamental solutions of these higher-order equations. Interestingly, it is shown that in the third-order case, a genuine non-negative real-valued probability distribution is obtained.
| Original language | English |
|---|---|
| Pages (from-to) | 209-223 |
| Number of pages | 15 |
| Journal | Stochastic Processes and their Applications |
| Volume | 85 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Feb 2000 |
Keywords
- Airy functions
- Brownian motion
- Feynman-Kac functional
- Higher-order heat-type equations
- Laplace transforms
- Maximal distribution
- Signed measures
- Stable laws