Valentin Konakov

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We study the sensitivity of the densities of non degenerate diffusion processes and related Markov Chains with respect to a perturbation of the coefficients. Natural applications of these results appear in models with misspecified coefficients or for the investigation of the weak error of the Euler scheme with irregular coefficients. Résumé. Nous étudions(More)
RATIONALE Zirconia doped with a lanthanum oxide system is of high interest due to its exceptional thermal stability for the development of high performance ceramics. It possesses the beneficial properties of pure zirconia, such as heat resistance, mechanical strength and inertness, but also eliminates its main disadvantage, i.e. brittleness. At high(More)
1 Abstract Let X 1 ;. . .; X N be independent and identically distributed random variables with a continuous probability density function f. We compare tests for the decision between the simple hypothesis H : f = f 0 against K : f 6 = f 0 and calculate the power for local alternatives. In contrast to the traditional minimax setting we consider a non-minimax(More)
We consider triangular arrays of Markov chains that converge weakly to a diffusion process. Second order Edgeworth type expansions for transition densities are proved. The paper differs from recent results in two respects. We allow nonhomogeneous diffusion limits and we treat transition densities with time lag converging to zero. Small time asymptotics are(More)
We study the weak error associated with the Euler scheme of non degenerate diffusion processes with non smooth bounded coefficients. Namely, we consider the cases of Hölder continuous coefficients as well as piecewise smooth drifts with smooth diffusion matrices. 1991 Mathematics Subject Classification. Primary 60H10; Secondary 65C30. December 22, 2016.
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