Limit theorem for the number of crossings of a strip by the Levy process with small drift
Limit theorem for the number of crossings of a strip by the Levy process with small drift
(Russian, English abstract)
Siberian Electronic Mathematical Reports, 21, 2, pp. 1295-1313 (2024)
Abstract:
We study the distribution of the crossings number of a strip by trajectories of a stationary stochastic process with independent increments (the Levy process). Assuming that negative drift of the process tends to zero, we establish the convergence of the distribution of the crossings number to the
exponential one under appropriate normalization.
Keywords: stochastic process with independent increments (Levy process), number of strip crossings, limit theorems