Approximation at first and second order of -order integrals of the fractional Brownian motion and of certain semimartingales.
Milstein’s type schemes for fractional SDEs
Weighted power variations of fractional brownian motion are used to compute the exact rate of convergence of some approximating schemes associated to one-dimensional stochastic differential equations (SDEs) driven by . The limit of the error between the exact solution and the considered scheme is computed explicitly.
Existence and asymptotic behaviour of some time-inhomogeneous diffusions
Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient . This process can be viewed as a Brownian motion evolving in a potential, possibly singular, depending on time. We prove results on the existence and uniqueness of solution, study its asymptotic behaviour and made a precise description, in terms of parameters , and , of the recurrence, transience and convergence. More precisely, asymptotic...
Singularités des fonctions de Green hypoelliptiques
A singular large deviations phenomenon
Hölder norms and the support theorem for diffusions
m-order integrals and generalized Itô's formula ; the case of a fractional brownian motion with any Hurst index
Abel transform and integrals of Bessel local times
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