Cutoff stability of multivariate geometric Brownian motion

G. Barrera; M. A. Högele; J. C. Pardo

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arXiv · 2207.01666

Cutoff stability of multivariate geometric Brownian motion

G. Barrera·M. A. Högele·J. C. Pardo

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Abstract

This article establishes cutoff convergence or abrupt convergence of three statistical quantities for multivariate (Hurwitz) stable geometric Brownian motion: the autocorrelation function, the Wasserstein distance between the current state and its degenerate limiting measure, and, finally, anti-concentration probabilities, which yield a fine-tuned trade-off between almost sure rates and the respective integrability of the random modulus of convergence using a quantitative Borel--Cantelli Lemma. We obtain in case of simultaneous diagonalizable drift and volatility matrices a complete representation of the mean square and derive nontrivial, sufficient and necessary mean square stability conditions, which include all real and imaginary parts of the volatility matrices' spectra.

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BibTeX RIS

G. Barrera, M. A. Högele, J. C. Pardo. 2022-07-04. Cutoff stability of multivariate geometric Brownian motion. https://arxiv.org/abs/2207.01666

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