This paper is concerned with the problem of simulation of ${\left({X}_{t}\right)}_{0\le t\le T}$, the solution of a stochastic differential equation constrained by some boundary conditions in a smooth domain $D$: namely, we consider the case where the boundary $\partial D$ is killing, or where it is instantaneously reflecting in an oblique direction. Given $N$ discretization times equally spaced on the interval $[0,T]$, we propose new discretization schemes: they are fully implementable and provide a weak error of order ${N}^{-1}$ under some conditions. The construction...

This paper is concerned with the problem of simulation of , the
solution of a stochastic differential equation constrained by some boundary conditions in a smooth domain
: namely, we consider the case where the boundary is killing, or where it is instantaneously
reflecting in an oblique direction. Given discretization times equally spaced on the interval ,
we propose new discretization schemes: they are fully implementable and provide a weak error of order
under some conditions....

In this paper we prove the Local Asymptotic Mixed Normality (LAMN) property for the statistical model given by the observation of local means of a diffusion process . Our data are given by
d() for =0, …, −1 and the unknown parameter appears in the diffusion coefficient of the process only. Although the data are neither markovian nor gaussian we can write down, with help of Malliavin calculus, an explicit expression for the log-likelihood...

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