H−C1 Maps and elliptic SPDEs with polynomial and exponential perturbations of Nelson's Euclidean free field

AbstractElliptic stochastic partial differential equations (SPDE) with polynomial and exponential perturbation terms defined in terms of Nelson's Euclidean free field on Rd are studied using results by S. Kusuoka and A.S. Üstünel and M. Zakai concerning transformation of measures on abstract Wiener space. SPDEs of this type arise, in particular, in (Euclidean) quantum field theory with interactions of the polynomial or exponential type. The probability laws of the solutions of such SPDEs are given by Girsanov probability measures, that are non-linearly transformed measures of the probability law of Nelson's free field defined on subspaces of Schwartz space of tempered distributions

Second-order asymptotic expansion for a non-synchronous covariation estimator

In this paper, we consider the problem of estimating the covariation of two diffusion processes when observations are subject to non-synchronicity. Building on recent papers \cite{Hay-Yos03, Hay-Yos04}, we derive second-order asymptotic expansions for the distribution of the Hayashi-Yoshida estimator in a fairly general setup including random sampling schemes and non-anticipative random drifts. The key steps leading to our results are a second-order decomposition of the estimator's distribution in the Gaussian set-up, a stochastic decomposition of the estimator itself and an accurate evaluation of the Malliavin covariance. To give a concrete example, we compute the constants involved in the resulting expansions for the particular case of sampling scheme generated by two independent Poisson processes

Convergence of Dirichlet forms and associated Schroedinger operators

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