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Article
Nonlinear trend exclusion procedure for models defined by stochastic differential and difference equations
We consider a diffusion process and its approximation with a Markov chain whose trends contain a nonlinear unbounded component. The usual parametrix method is inapplicable here since the trend is unbounded. We...
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Article
Linear trend exclusion for models defined with stochastic differential and difference equations
We consider a sequence of Markov chains that weakly converge to a diffusion process. We assume that the trend contains a linearly growing component. The usual parametrix method does not apply since the trend i...
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Article
Diffusion processes on solvable groups of upper triangular 2×2 matrices and their approximation
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Article
Log-classes for the increments of a multivariate empirical process
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Article
Extrema of some Gaussian processes with large trends and density estimation inL ∞ norm
Let {μ n (t),t ∈ [O,T n ]} be the sequence of trends andX n − μ n (t) is ...
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Article
Local limit theorems on the convergence of Markov chains to diffusion processes
One proves the uniform convergence of the densities of the finite-dimensional distributions of certain families of Markov chains to the densities of the finite-dimensional distributions of a nondegenerate diff...
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Chapter and Conference Paper
Approximations of deviation fields of some nonparametic statistical estimates by gaussian fields, invariance principles
