The Onsager-Machlup functional associated with additive fractional noise (to be submitted.)
Consider the solution of a stochastic differential equation in which the noise is a fractional Brownian motion. This is a continuous-time random path that is almost surely continuous. The probability that this path turns out to be exactly equal to one prescribed deterministic path is zero. However, it turns out that there are special deterministic paths near which this random path can remain with positive probability. This is quantified by the Onsager-Machlup functional of the special deterministic path.
S. Moret and D. Nualart computed the functional for regular enough paths in the one-dimensional case. In this paper I compute the Onsager-Machlup functional for all paths (that are special in that they exhibit the suitable behavior) in the multidimensional case.