Ornstein-Uhlenbeck Processes of Bounded Variation
| Autor: | Nikita Ratanov |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Statistics and Probability
Distribution (number theory) General Mathematics Probability (math.PR) 010102 general mathematics Mathematical analysis Ornstein–Uhlenbeck process 01 natural sciences Langevin equation 010104 statistics & probability Mathematics::Probability Joint probability distribution Bounded variation FOS: Mathematics 60J75 60J27 60K99 Limit (mathematics) 0101 mathematics Telegraph process Mathematics - Probability Brownian motion Mathematics |
| Zdroj: | Methodology and Computing in Applied Probability. 23:925-946 |
| ISSN: | 1573-7713 1387-5841 |
| Popis: | Ornstein-Uhlenbeck process of bounded variation is introduced as a solution of an analogue of the Langevin equation with an integrated telegraph process replacing a Brownian motion. There is an interval $I$ such that the process starting from the internal point of $I$ always remains within $I$. Starting outside, this process a. s. reaches this interval in a finite time. The distribution of the time for which the process falls into this interval is obtained explicitly. The certain formulae for the mean and the variance of this process are obtained on the basis of the joint distribution of the telegraph process and its integrated copy. Under Kac's rescaling, the limit process is identified as the classical Ornstein-Uhlenbeck process. 23 pages |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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