Moment generating function of a first hitting place for the integrated Ornstein-Uhlenbeck process
نویسندگان
چکیده
منابع مشابه
First Hitting Place Probabilities for a Discrete Version of the Ornstein-Uhlenbeck Process
A Markov chain with state space {0, . . . ,N} and transition probabilities depending on the current state is studied. The chain can be considered as a discrete Ornstein-Uhlenbeck process. The probability that the process hitsN before 0 is computed explicitly. Similarly, the probability that the process hits N before −M is computed in the case when the state space is {−M, . . . , 0, . . . ,N} an...
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Three expressions are provided for the first hitting time density of an Ornstein-Uhlenbeck process to reach a fixed level. The first hinges on an eigenvalue expansion involving zeros of the parabolic cylinder functions. The second is an integral representation involving some special functions whereas the third is given in terms of a functional of a 3-dimensional Bessel bridge. The expressions a...
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Also, a process {Yt : t ≥ 0} is said to have independent increments if, for all t0 < t1 < . . . < tn, the n random variables Yt1 − Yt0 , Yt2 − Yt1 , ..., Ytn − Ytn−1 are independent. This condition implies that {Yt : t ≥ 0} is Markovian, but not conversely. The increments are further said to be stationary if, for any t > s and h > 0, the distribution of Yt+h− Ys+h is the same as the distributio...
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ژورنال
عنوان ژورنال: Stochastic Processes and their Applications
سال: 1989
ISSN: 0304-4149
DOI: 10.1016/0304-4149(89)90080-x