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Analysis of the discrete Ornstein-Uhlenbeck process caused by the tick size effect. (English) Zbl 1296.60228

The author introduces a discrete version of the Ornstein-Uhlenbeck (OU) process and discusses its properties. The construction of this discrete process is motivated by the discrete effect of the thick size at financial markets and it is based on matching of the first two moments across an infinitesimal interval. The discrete process converges to the continuous OU process in the second order of step size. The author also finds the closed loop formula for the moment generating function of the discrete OU process and discusses its properties for any time horizon including steady state. The steady state probability distribution is completely characterized, too.

MSC:

60J75 Jump processes (MSC2010)
60G20 Generalized stochastic processes
60J27 Continuous-time Markov processes on discrete state spaces
60G15 Gaussian processes
91B26 Auctions, bargaining, bidding and selling, and other market models
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References:

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