相关论文: A note on the Moment of Complex Wiener-Ito Integra…
We prove sufficient conditions, ensuring that a sequence of multiple Wiener-It\^{o} integrals (with respect to a general Gaussian process) converges stably to a mixture of normal distributions. Our key tool is an asymptotic decomposition of…
We present the product formula for complex multiple Wiener-Ito integrals. As applications, we show the Ustunel-Zakai independent criterion, the Nourdin-Rosinski asymptotic moment-independent criterion and joint convergence criterion for…
In 2005, Nualart and Peccati showed that, surprisingly, the convergence in distribution of a normalized sequence of multiple Wiener-It\^o integrals towards a standard Gaussian law is equivalent to convergence of just the fourth moment to 3.…
We obtain strong consistency and asymptotic normality of a least squares estimator of the drift coefficient for complex-valued Ornstein-Uhlenbeck processes disturbed by fractional noise, extending the result of Y. Hu and D. Nualart,…
We investigate the optimal rate of convergence in the multidimensional normal approximation of vector-valued Wiener-Ito integrals of which components all belong to the same fixed Wiener chaos. Combining Malliavin calculus, Stein's method…
We clearly characterize the relation between real and complex Wiener-Ito integrals. Given a complex multiple Wiener-Ito integral, we get explicit expressions for two kernels of its real and imaginary parts. Conversely, consider a…
For a series of univariate or multivariate complex multiple Wiener-It\^o integrals, we appreciably improve the previously known contractions condition of complex Fourth Moment Theorem (FMT) and present a fourth moment type Berry-Ess\'een…
We establish several contraction formulas for Kirchhoff index. We relate Kirchhoff index with some other metrized graph invariants. By applying our contraction formulas successively when the graph is a tree, we derive new formulas for…
We establish explicit bounds on the convex distance between the distribution of a vector of smooth functionals of a Gaussian field, and that of a normal vector with a positive definite covariance matrix. Our bounds are commensurate to the…
We conjecture the full asymptotic expansion of a product of Riemann zeta functions, evaluated at the non-trivial zeros of the zeta function, with shifts added in each argument. By taking derivatives with respect to these shifts, we form a…
We compute the deterministic approximation for mixed fluctuation moments of products of deterministic matrices and general Sobolev functions of Wigner matrices. Restricting to polynomials, our formulas reproduce recent results of [Male,…
The main solutions in sense of Kantorovich of nonlinear Volterra operator-integral equations are constructed. Convergence of the successive approximations is established through studies of majorant integral and majorant algebraic equations.…
It is shown that a contraction on a Hilbert space is complex symmetric if and only if the values of its characteristic function are all symmetric with respect to a fixed conjugation. Applications are given to the description of complex…
The paper presents new and known results on estimates of important linear and nonlinear approximation characteristics of generalized Wiener classes of functions of several variables in different metrics.
The subject of the present study is the Monte Carlo path-integral evaluation of the moments of spectral functions. Such moments can be computed by formal differentiation of certain estimating functionals that are infinitely-differentiable…
We give a new characterization for the convergence in distribution to a standard normal law of a sequence of multiple stochastic integrals of a fixed order with variance one, in terms of the Malliavin derivatives of the sequence. We extend…
We present a characterization of the null moments of the Complex Multivariate Normal Distribution with non-singular covariance matrix and we give closed-forms expressions for its non-null moments.
On symplectic manifolds, we introduce a Morse-type complex with elements generated by pairs of critical points of a Morse function. The differential of the complex consists of gradient flows and an integration of the symplectic structure…
Complexiton solutions (or complexitons for short) are exact solutions newly introduced to integrable equations. Starting with the solution classification for a linear differential equation, the Korteweg-de Vries equation and the Toda…
This paper communicates recent results in theory of complex symmetric operators and shows, through two non-trivial examples, their potential usefulness in the study of Schr\"odinger operators. In particular, we propose a formula for…