| Abstract: |
| Consider ``stochastic differential equations driven by
fractional Brownian motion with Hurst parameter $H\in (1/4, 1)$.
Their solutions are sometimes called fractional diffusion processes.
The main purpose of this talk is conditioning these processes to reach a given terminal point.
We call the conditioned processes fractional diffusion bridges.
Our main tool for mathematically rigorous conditioning
is quasi-sure analysis, which is a potential theoretic part of Malliavin calculus.
We also prove a small-noise large deviation principle
of Freidlin-Wentzell type for scaled fractional diffusion bridges
under a mild ellipticity assumption on the coefficient vector fields. |
|