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Lack of Gaussian Tail for integrals along fractional Brownian motions

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SSDW05 - Modelling and Applications of Anomalous Diffusions

A result of Kusuoka and Stroock states that the solutions to elliptic stochastic differential solutions, where vector fields have uniformly bounded derivatives of all orders, have Gaussian tails. For rough differential equations driven by fractional Brownian motions with Hurst parameter H and with same assumptions on vector fields as before, a celebrated result of Cass-Littterer-Lyons established a max(1+2H,1/2)-Weibull upper bound for the tail probability of the solution. Establishing a general lower bound seems difficult but we will discuss the particular case of integral along fractional Brownian motions of smooth functions with uniformly bounded and non degenerate derivatives of all orders. Joint work with Xi Geng. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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