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

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

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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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.
Stichworte
Levy processes; Stable processes; First passage times; Absolute; continuity
Erscheinungsjahr
2016
Zeitschriftentitel
JOURNAL OF THEORETICAL PROBABILITY
Band
29
Ausgabe
3
Seite(n)
776-796
ISSN
0894-9840
eISSN
1572-9230
Page URI
https://pub.uni-bielefeld.de/record/2906187

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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.

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