We prove almost sure convergence for the logarithmic average of f(W(X(t))/ψ(t)), where f is a suitable function, ψ(t) is a norming factor, W is a Wiener process and X is a suitable process, independent of W. Particular attention is paid for the case when X is the local time of a Wiener process or a reflected Wiener process.
- Iterated processes
- Logarithmic averages
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty