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Asymptotic behaviour and functional limit theorems for a time changed Wiener process

Author

Listed:
  • Kondratiev, Yuri
  • Mishura, Yuliya
  • Schilling, René L.

Abstract

We study the asymptotic behaviour of a properly normalized time changed Wiener processes. The time change reflects the fact that we consider the Laplace operator (which generates a Wiener process) multiplied by a possibly degenerate state-space dependent intensity λ(x). Applying a functional limit theorem for the superposition of stochastic processes, we prove functional limit theorems for the normalized time changed Wiener process. The normalization depends on the asymptotic behaviour of the intensity function λ. One of the possible limits is a skew Brownian motion.

Suggested Citation

  • Kondratiev, Yuri & Mishura, Yuliya & Schilling, René L., 2021. "Asymptotic behaviour and functional limit theorems for a time changed Wiener process," Statistics & Probability Letters, Elsevier, vol. 170(C).
    • Handle: RePEc:eee:stapro:v:170:y:2021:i:c:s016771522030300x
    DOI: 10.1016/j.spl.2020.108997
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