The First Passage Time of a Stable Process Conditioned to Not Overshoot

Cordero F (2016)
JOURNAL OF THEORETICAL PROBABILITY 29(3): 776-796.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
Consider a stable L,vy process and let , for , denote the first passage time of above the level . In this work, we give an alternative proof of the absolute continuity of the law of and we obtain a new expression for its density function. Our constructive approach provides a new insight into the study of the law of . The random variable , defined as the limit of when the corresponding overshoot tends to , plays an important role in obtaining these results. Moreover, we establish a relation between the random variable and the dual process conditioned to die at . This relation allows us to link the expression of the density function of the law of presented in this paper to the already known results on this topic.
Erscheinungsjahr
Zeitschriftentitel
JOURNAL OF THEORETICAL PROBABILITY
Band
29
Zeitschriftennummer
3
Seite
776-796
ISSN
eISSN
PUB-ID

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Cordero F. The First Passage Time of a Stable Process Conditioned to Not Overshoot. JOURNAL OF THEORETICAL PROBABILITY. 2016;29(3):776-796.
Cordero, F. (2016). The First Passage Time of a Stable Process Conditioned to Not Overshoot. JOURNAL OF THEORETICAL PROBABILITY, 29(3), 776-796. doi:10.1007/s10959-014-0592-6
Cordero, F. (2016). The First Passage Time of a Stable Process Conditioned to Not Overshoot. JOURNAL OF THEORETICAL PROBABILITY 29, 776-796.
Cordero, F., 2016. The First Passage Time of a Stable Process Conditioned to Not Overshoot. JOURNAL OF THEORETICAL PROBABILITY, 29(3), p 776-796.
F. Cordero, “The First Passage Time of a Stable Process Conditioned to Not Overshoot”, JOURNAL OF THEORETICAL PROBABILITY, vol. 29, 2016, pp. 776-796.
Cordero, F.: The First Passage Time of a Stable Process Conditioned to Not Overshoot. JOURNAL OF THEORETICAL PROBABILITY. 29, 776-796 (2016).
Cordero, Fernando. “The First Passage Time of a Stable Process Conditioned to Not Overshoot”. JOURNAL OF THEORETICAL PROBABILITY 29.3 (2016): 776-796.