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SUMMARY:Lack of Gaussian Tail for integrals along fractional Brownian moti
 ons - Horatio Boedihardjo (University of Warwick)
DTSTART:20240904T131500Z
DTEND:20240904T140000Z
UID:TALK217606@talks.cam.ac.uk
DESCRIPTION:A result of Kusuoka and Stroock states that the solutions to e
 lliptic stochastic differential solutions\, where vector fields have unifo
 rmly bounded derivatives of all orders\, have Gaussian tails. For rough di
 fferential equations driven by fractional Brownian motions with Hurst para
 meter H and with same assumptions on vector fields as before\, a celebrate
 d result of Cass-Littterer-Lyons established a max(1+2H\,1/2)-Weibull uppe
 r bound for the tail probability of the solution. Establishing a general l
 ower bound seems difficult but we will discuss the particular case of inte
 gral along fractional Brownian motions of smooth functions with uniformly 
 bounded and non degenerate derivatives of all orders. Joint work with Xi G
 eng.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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