Tail probabilities of local times of Gaussian processes and diffusions (Q2752177)

The authors study upper tail asymptotics for the local time at zero of linear Gaussian processes and diffusions. The main result states that in the Gaussian case (under certain conditions including an assumption of local nondeterminism) \(-\log P\{ \ell(0,1)>x\} \asymp 1/\sigma^{-1}(1/x)\), where \(\ell(0,1)\) is the local time in zero at time 1 and \(\sigma^2(h)=E\{(X(t+h)-X(t))^2\}\). In the case of linear diffusions the tails depend on the index of variation of the Green's function.NEWLINENEWLINEFor the entire collection see [Zbl 0964.00044].