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A note on first passage probabilities of a Lévy process reflected at a general barrier

Palmowski Z., Świątek P.

Probability and Mathematical Statistics

2017

Vol. 37, Fasc. 2

455--469

In this paper we analyze a Lévy process reflected at a general (possibly random) barrier. For this process we prove the Central Limit Theorem for the first passage time.We also give the finite-time first passage probability asymptotics.

Central limit theorems for random stain

Ebrahim H. H.

Probability and Mathematical Statistics

2004

Vol. 24, Fasc. 2

321--338

The Central Limit Theorem in R and Rn is proved for two-parameter stochastic process proposed in [6] as a model of a stain of pollution.