For [mu]=([mu]1,...,[mu]d) with each [mu]i being a signed measure on belonging to the Kato class , a diffusion with drift [mu] is a diffusion process in whose generator can be formally written as L+[mu][dot operator][backward difference] where L is a uniformly elliptic differential operator....

It is known that in the critical case the conditional least squares estimator (CLSE) of the offspring mean of a discrete time branching process with immigration is not asymptotically normal. If the offspring variance tends to zero, it is normal with normalization factor n2/3. We study a...

We prove the existence of the unique solution of a general backward stochastic differential equation with quadratic growth driven by martingales. A kind of comparison theorem is also proved.

We consider a mass-conservative fragmentation of the unit interval. Motivated by a result of Berestycki [J. Berestycki, Multifractal spectra of fragmentation processes, J. Statist. Phys. 113 (3-4) (2003) 411-430], the main purpose of this work is to specify the Hausdorff dimension of the set...

We study the asymptotic performance of approximate maximum likelihood estimators for state space models obtained via sequential Monte Carlo methods. The state space of the latent Markov chain and the parameter space are assumed to be compact. The approximate estimates are computed by, firstly,...

Let M be a complete Riemannian manifold and [mu] the distribution of the diffusion process generated by where Z is a C1-vector field. When is bounded below and Z has, for instance, linear growth, the transportation-cost inequality with respect to the uniform distance is established for [mu] on...

We treat an extension of Jacod's theorem for initial enlargement of filtrations with respect to random times. In Jacod's theorem the main condition requires the absolute continuity of the conditional distribution of the random time with respect to a nonrandom measure. Examples appearing in the...

Recent optimal scaling theory has produced a condition for the asymptotically optimal acceptance rate of Metropolis algorithms to be the well-known 0.234 when applied to certain multi-dimensional target distributions. These d-dimensional target distributions are formed of independent components,...

A dynamical system perturbed by white noise in a neighborhood of an unstable fixed point is considered. We obtain the exit asymptotics in the limit of vanishing noise intensity. This is a refinement of a result by Kifer (1981).

We consider the stochastic volatility model with B a Brownian motion and [sigma] of the form where WH is a fractional Brownian motion, independent of the driving Brownian motion B, with Hurst parameter H=1/2. This model allows for persistence in the volatility [sigma]. The parameter of interest...