We give a result of stability in law of the local time of the fractional Brownian motion with respect to small perturbations of the Hurst parameter. Concretely, we prove that the law (in the space of continuous functions) of the local time of the fractional Brownian motion with Hurst parameter H converges weakly to that of the local time of \(B^{H_0}\), when H tends to H 0.
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References
Berman S.M. (1969). Local times and sample function properties of stationary Gaussian processes. Trans. Am. Math. Soc. 137, 277–299
Berman S.M. (1970). Gaussian processes with stationary increments: local times and sample function properties. Ann. Math. Stat. 41, 1260–1272
Berman, S. M. (1973). Local nondeterminism and local times of Gaussian processes. Indiana Univ. Math. J. 23, 69–94, 1973/74.
Billingsley P. (1968). Convergence of Probability Measures. Wiley, New York
Yor, M. (1983). Le drap brownien comme limite en loi de temps locaux linéaires. In Seminar on Probability, XVII, Lecture Notes in Math., Vol. 986. Springer, Berlin, pp. 89–105.
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Jolis, M., Viles, N. Continuity in Law with Respect to the Hurst Parameter of the Local Time of the Fractional Brownian Motion. J Theor Probab 20, 133–152 (2007). https://doi.org/10.1007/s10959-007-0054-5
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DOI: https://doi.org/10.1007/s10959-007-0054-5