Ornstein-Uhlenbeck Processes of Bounded Variation

Nikita Ratanov

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

1 Cita (Scopus)

Resumen

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.

Idioma originalInglés estadounidense
PublicaciónMethodology and Computing in Applied Probability
DOI
EstadoEn prensa - 2020

All Science Journal Classification (ASJC) codes

  • Estadística y probabilidad
  • Matemáticas (todo)

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