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Coupling distances between Lévy measures and applications to noise sensitivity of SDE

    https://doi.org/10.1142/S0219493715500094Cited by:5 (Source: Crossref)

    We introduce the notion of coupling distances on the space of Lévy measures in order to quantify rates of convergence towards a limiting Lévy jump diffusion in terms of its characteristic triplet, in particular in terms of the tail of the Lévy measure. The main result yields an estimate of the Wasserstein–Kantorovich–Rubinstein distance on path space between two Lévy diffusions in terms of the coupling distances. We want to apply this to obtain precise rates of convergence for Markov chain approximations and a statistical goodness-of-fit test for low-dimensional conceptual climate models with paleoclimatic data.

    AMSC: 60J60, 60J75, 60F17, 60G51, 60H10, 62G32, 62P12

    References

    • L. Arnold, Stochastic Climate Models, eds. P. Imkelleret al. (Birkhäuser, 2001) pp. 141–157. CrossrefGoogle Scholar
    • R.   Benzi et al. , Tellus   34 , 10 ( 1982 ) . CrossrefGoogle Scholar
    • N.   Berglund and D.   Landon , Nonlinearity   25 , 2303 ( 2012 ) . Crossref, ISIGoogle Scholar
    • N.   Berglund and B.   Gentz , Stoch. Dyn.   2 , 327 ( 2002 ) . LinkGoogle Scholar
    • R.   Boisvert et al. , NIST Handbook of Mathematical Functions ( Cambridge Univ. Press , 2010 ) . Google Scholar
    • A.   Debussche , M.   Högele and P.   Imkeller , The Dynamics of Non-linear Reaction–Diffusion Equations with Small Lévy Noise , Springer Lecture Notes in Mathematics   2085 ( Springer , 2013 ) . CrossrefGoogle Scholar
    • P. D.   Ditlevsen , Geophys. Res. Lett.   26 , 1441 ( 1999 ) . Crossref, ISIGoogle Scholar
    • C. Doss and M. Thieullen, Oscillations and random perturbations of a FitzHugh–Nagumo system, Preprint hal-00395284, 2009 . Google Scholar
    • R. M.   Dudley , Real Analysis and Probability ( Cambridge Univ. Press , 2004 ) . Google Scholar
    • J. Gairing, M. Högele, T. Kosenkova and A. Kulik, On the calibration of Lévy driven time series with coupling distances — An application in paleoclimate, submitted to INDAM Vol. Mathematical Paradigms in Climate Science, http://www.math.uni-potsdam.de/Jpreprint/2014.html . Google Scholar
    • J. Gairing and P. Imkeller, Stable CLTs and rates for power variation of α-stable Lévy processes, to appear in Method. Comput. Appl. Probab . Google Scholar
    • B. V.   Gnedenko and A. N.   Kolmogorov , Limit Distributions for Sums of Independent Random Variables ( Addison-Wesley , 1968 ) . Google Scholar
    • K.   Hasselmann , Tellus   28 , 473 ( 1976 ) . CrossrefGoogle Scholar
    • C.   Hein , P.   Imkeller and I.   Pavlyukevich , Interdisciplinary Math. Sci.   8 , 137 ( 2009 ) . Link, ISIGoogle Scholar
    • M.   Högele and I.   Pavlyukevich , Stoch. Anal. Appl.   32 , 163 ( 2014 ) . Crossref, ISIGoogle Scholar
    • N.   Ikeda and S.   Watanabe , Stochastic Differential Equations and Diffusion Processes ( North-Holland , 1981 ) . Google Scholar
    • P.   Imkeller and A.   Monahan , Stoch. Dyn.   2 , 311 ( 2002 ) . LinkGoogle Scholar
    • P.   Imkeller , Prog. Probab.   49 , 213 ( 2001 ) . Google Scholar
    • P.   Imkeller and I.   Pavlyukevich , Stoch. Process. Appl.   116 , 611 ( 2006 ) . Crossref, ISIGoogle Scholar
    • P.   Imkeller and I.   Pavlyukevich , ESAIM: Probab. Statist.   12 , 412 ( 2008 ) . CrossrefGoogle Scholar
    • P.   Imkeller , I.   Pavlyukevich and T.   Wetzel , Ann. Probab.   37 , 530 ( 2009 ) . Crossref, ISIGoogle Scholar
    • V. S.   Koroliuk , N.   Limnios and I. V.   Samoilenko , Th. Probab. Math. Statist.   80 , 85 ( 2009 ) . Google Scholar
    • T.   Kosenkova , Th. Stoch. Process.   18 , 86 ( 2012 ) . Google Scholar
    • T.   Kosenkova , Nature   431 , 147 ( 2004 ) . Crossref, ISIGoogle Scholar
    • I.   Pavlyukevich , Stoch. Dyn.   11 , 495 ( 2011 ) . Link, ISIGoogle Scholar
    • S. T.   Rachev and L.   Rüschendorf , Mass Transportation Problems, Vol. I: Theory, Vol. II: Applications ( Springer-Verlag , 1998 ) . Google Scholar
    • H. C.   Tuckwell , R.   Rodriguez and F. Y. M.   Wan , Neural Comput.   15 , 143 ( 2003 ) . Crossref, ISIGoogle Scholar