2004/08/13 by Marina Kozlova, Kozlova, Marina, Paavo Salminen +1
Economics, Econometrics and Finance · Mathematics · #60G10 #60J60 #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #advanced mathematical theories #math.PR #msc:60G10 #msc:60J60
paper · pdf · doi:10.48550/arxiv.math/0408178
32 pages; extended abstract
openalex publication_date 2004/08/13 · arxiv created 2004/08/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper excursions of a stationary diffusion in stationary state are studied. In particular, we compute the joint distribution of the occupation times I(+)t and I(-)t above and below, respectively, the observed level at time t during an excursion. We consider also the starting time gt and the ending time dt of the excursion (straddling t) and discuss their relations to the Levy measure of the inverse local time. It is seen that the pairs (I(+)t, I(-)t) and (t-gt, dt-t) are identically distributed. Moreover, conditionally on I(+)t + I(-)t =v, the variables I(+)t and I(-)t are uniformly distributed on (0,v). Using the theory of the Palm measures, we derive an analoguous result for excursion bridges.