We consider the following hidden Markov chain problem: estimate the finite-dimensional parameter [theta] in the equation when we observe discrete data Xi/n at times i=0,...,n from the diffusion . The processes (Wt)t[set membership, variant][0,1] and (Bt)t[set membership, variant][0,1] are two...

We study the nonparametric estimation of the coefficients of a 1-dimensional diffusion process from discrete observations. Different asymptotic frameworks are considered. Minimax rates of convergence are studied over a wide range of Besov smoothness classes. We construct estimators based on...

We relate the Lp-variation, 2≤p∞, of a solution of a backward stochastic differential equation with a path-dependent terminal condition to a generalized notion of fractional smoothness. This concept of fractional smoothness takes into account the quantitative propagation of singularities in...

For a stopped diffusion process in a multidimensional time-dependent domain , we propose and analyse a new procedure consisting in simulating the process with an Euler scheme with step size [Delta] and stopping it at discrete times in a modified domain, whose boundary has been appropriately...

We study the -time regularity of the Z-component of a Markovian BSDE, whose terminal condition is a function g of a forward SDE (Xt)0=t=T. When g is Lipschitz continuous, Zhang (2004) [18] proved that the related squared -time regularity is of order one with respect to the size of the time mesh....

We study the error induced by the time discretization of decoupled forward-backward stochastic differential equations (X,Y,Z). The forward component X is the solution of a Brownian stochastic differential equation and is approximated by a Euler scheme XN with N time steps. The backward component...

We are interested in approximating a multidimensional hypoelliptic diffusion process (Xt)t[greater-or-equal, slanted]0 killed when it leaves a smooth domain D. When a discrete Euler scheme with time step h is used, we prove under a noncharacteristic boundary condition that the weak error is...

We study the weak approximation of a multidimensional diffusion (Xt)0[less-than-or-equals, slant]t[less-than-or-equals, slant]T killed as it leaves an open set D, when the diffusion is approximated by its continuous Euler scheme or by its discrete one , with discretization step T/N. If we set...

We derive expansion results in order to approximate the law of the average of the marginal of diffusion processes. The average is computed w.r.t. a general parameter that is involved in the diffusion dynamics. Our approximation is based on the use of proxys with normal distribution or log-normal...

For n equidistant observations of a Lévy process at time distance Δn we consider the problem of testing hypotheses on the volatility, the jump measure and its Blumenthal–Getoor index in a non- or semiparametric manner. Asymptotically as n→∞ we allow for both, the high-frequency regime...