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This paper is concerned with the analysis of the average error in approximating the global minimum of a 1-dimensional, time-homogeneous diffusion by non-adaptive methods. We derive the limiting distri...
We develop exact Markov chain Monte Carlo methods for discretely-sampled, directly and indirectly observed diffusions. The qualification "exact" refers to the fact that the invariant and limiting dist...
It has recently been shown that there are grave differences in the regularity behavior of the empirical process based on scalar diffusions as compared to the classical empirical process, due to the e...
We study the problem of estimating parameters of the limiting equation of a multiscale diffusion in the case of averaging and homogenization, given data from the corresponding multiscale system. Fir...
Large deviations of invariant measures for degenerate diffusions
We investigate stability, with respect to convergence of coefficients, of one-dimensional It6 diRussions as well as one-dimensionat diffusions wrresponding to second order divergence form operators....
We consider a time-inhomogeneous Markov family (X, P,3 corresponding to a symmetric uniformly elliptic divergence form operator. We show that for any rp in the Sobolev space W: n Wi with p = 2 if d...
In the present article we consider a model of motion of a passive tracer particle under a random, non-steady (time dependent), incompressible velocity flow in a medium with positive molecular diffus...
We study the equation of a motion of a passivc tracer in a time-independent turbulent flow in a medium with a positive molecular diffusivity. In [6] the authors have shown the existence of an invar...
Spatial branching processes became increasingly popular in the past decades, not only because of their obvious connection to biology, but also because superprocesses are intimately related to nonlinea...
We study the dynamical properties of the Brownian diffusions having σ Id as diffusion coefficient matrix and b=∇U as drift vector. We characterize this class through the equality D+2=D-2, where ...
Bounds on the large deviations probability of the maximum likelihood estimator and regular Bayes estimators, and Berry–Esseen type bound for the suitably normalized maximum likelihood estimator of a...
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 X. Our data are given by R 10 Xs...
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability ...

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