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Titel:

Rate-optimal estimation of mixed semimartingales

Dokumenttyp:
Zeitschriftenaufsatz
Autor(en):
Chong, Carsten; Delerue, Thomas; Mies, Fabian
Abstract:
Consider the sum Y=B+B(H) of a Brownian motion B and an independent fractional Brownian motion B(H) with Hurst parameter H∈(0,1). Surprisingly, even though B(H) is not a semimartingale, Cheridito proved in [Bernoulli 7 (2001) 913--934] that Y is a semimartingale if H>3/4. Moreover, Y is locally equivalent to B in this case, so H cannot be consistently estimated from local observations of Y. This paper pivots on a second surprise in this model: if B and B(H) become correlated, then Y will never b...     »
Dewey Dezimalklassifikation:
510 Mathematik
Zeitschriftentitel:
Preprint
Jahr:
2022
Sprache:
en
Volltext / DOI:
doi:10.48550/ARXIV.2207.10464
Verlag / Institution:
arXiv
Eingereicht (bei Zeitschrift):
21.07.2022
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