作者：Deya, Aurelien; Panloup, Fabien; Tindel, Samy
作者单位：Universite de Lorraine; Universite d'Angers; Purdue University System; Purdue University
摘要：We investigate the problem of the rate of convergence to equilibrium for ergodic stochastic differential equations driven by fractional Brownian motion with Hurst parameter H is an element of (1/3, 1) and multiplicative noise component sigma. When sigma is constant and for every H is an element of (0, 1), it was proved in [Ann. Probab. 33 (2005) 703-758] that, under some mean-reverting assumptions, such a process converges to its equilibrium at a rate of order t(-alpha) where alpha is an eleme...
作者：Chevyrev, Ilya; Friz, Peter K.
作者单位：University of Oxford; Technical University of Berlin; Leibniz Association; Weierstrass Institute for Applied Analysis & Stochastics
摘要：In the spirit of Marcus canonical stochastic differential equations, we study a similar notion of rough differential equations (RDEs), notably dropping the assumption of continuity prevalent in the rough path literature. A new metric is exhibited in which the solution map is a continuous function of the driving rough path and a so-called path function, which directly models the effect of the jump on the system. In a second part, we show that general multidimensional semimartingales admit canon...
