The search session has expired. Please query the service again.
We consider a diffusion process X which is observed at times i/n
for i = 0,1,...,n, each observation being subject to a measurement
error. All errors are independent and centered Gaussian with known
variance pn. There is an unknown parameter within the diffusion
coefficient, to be estimated. In this first paper the
case when X is indeed a Gaussian martingale is examined: we can prove
that the LAN property holds under quite weak smoothness assumptions,
with an explicit limiting Fisher information....
We consider a diffusion process which is observed at times for , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance . There is an unknown parameter to estimate within the diffusion coefficient. In this second paper we construct estimators which are asymptotically optimal when the process is a gaussian martingale, and we conjecture that they are also optimal in the general case.
We consider a diffusion process X which is observed at times i/n
for i = 0,1,...,n, each observation being subject to a measurement
error. All errors are independent and centered Gaussian with known
variance pn. There is an unknown parameter to estimate within the
diffusion coefficient. In this second paper we
construct estimators which are asymptotically optimal when the
process X is a Gaussian martingale, and we conjecture that they are
also optimal in the general case.
Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.By generalization of Ehrenfest’s urn model, we obtain discrete approximations
to spatially one-dimensional time-fractional diffusion processes with
drift towards the origin. These discrete approximations can be interpreted
(a) as difference schemes for the relevant time-fractional partial differential
equation, (b) as random walk models. The relevant convergence questions as
well as the behaviour for time tending to infinity...
Currently displaying 21 –
31 of
31