Penalizing fractional Brownian motion for being negative

Abstract

We study a modification of the fractional analogue of the Brownian meander, which is Brownian motion conditioned to be positive on the time interval $[0,1]$. More precisely, we determine the weak limit of a fractional Brownian motion which is penalized -- instead of being killed -- when leaving the positive half-axis. In the Brownian case, we give a representation of the limiting process in terms of an explicit SDE and compare it to the SDE fulfilled by the Brownian meander.

Minor corrections

References in corpus (2)

• Asymptotic behavior of self-affine processes in semi-infinite domains
• Persistence probabilities of two-sided (integrated) sums of correlated stationary Gaussian sequences

Cited by in corpus (1)

• On the speed of convergence of discrete Pickands constants to continuous ones