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On the first passage times of reflected O-U processes with two-sided barriers. (English) Zbl 1114.60047
The Laplace transform of the first passage times of reflected Ornstein-Uhlenbeck processes with two-sided barriers is given. The results are derived by means of solving the related boundary value problem for the differential infinitesimal operator of the strong Markov Ornstein-Uhlenbeck process and by applying the normal-reflection conditions at the reflecting barriers.
MSC:
60H10Stochastic ordinary differential equations
60G40Stopping times; optimal stopping problems; gambling theory
60J25Continuous-time Markov processes on general state spaces
60G15Gaussian processes
90B05Inventory, storage, reservoirs
References:
[1]S. Asmussen, Applied Probability and Queues, 2nd edn. (Springer, Berlin, 2003).
[2]M. Harrison, Brownian Motion and Stochastic Flow Systems. (John Wiley & Sons, New York, 1986).
[3]P. Lions and A. Sznitman, Stochastic differential equations with reflecting boundary conditions. Comm. Pure Appl. Math. 37 (1984) 511–537. · Zbl 0598.60060 · doi:10.1002/cpa.3160370408
[4]A. Ward and P. Glynn, A diffusion approximation for Markovian queue with reneging. Queueing Systems 43 (2003) 103–128. · Zbl 1054.60100 · doi:10.1023/A:1021804515162
[5]A. Ward and P. Glynn, Properties of the reflected Ornstein-Uhlenbeck process. Queueing Systems 44 (2003) 109–123. · Zbl 1026.60106 · doi:10.1023/A:1024403704190