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We obtain weighted $L^p$ inequalities for pseudo-differential operators with smooth symbols and their commutators by using a class of new weight functions which include Muckenhoupt weight functions. Our results improve essentially some…
The aim of this paper is to extend to the spaces L^2(R^d , (1+|v|)^2k dv) the spectral study led in L^2(R^d , exp(|v|^2/2)dv) by R. Ellis and M. Pinsky on the space inhomogeneous linearized Boltzmann operator for hard spheres. More…
We derive the limiting distributions of exceedances point processes of randomly scaled weakly dependent stationary Gaussian sequences under some mild asymptotic conditions. In the literature analogous results are available only for…
We study pseudo-differential operators on a wedge with continuous and variable discrete branching asymptotics.
In this paper, we present the asymptotic distribution of M-estimators for parameters in non-stationary AR(p) processes. The innovations are assumed to be in the domain of attraction of a stable law with index $0<\alpha\le2$. In particular,…
The spectral density function describes the second-order properties of a stationary stochastic process on $\mathbb{R}^d$. This paper considers the nonparametric estimation of the spectral density of a continuous-time stochastic process…
Discrete random probability measures are a key ingredient of Bayesian nonparametric inferential procedures. A sample generates ties with positive probability and a fundamental object of both theoretical and applied interest is the…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
One discusses a problem of asymptotical behavior for some operators in a general theory of pseudo differential equations on manifolds with borders. Using the distribution theory one obtains certain explicit representations for these…
For suitable families of locally infinitely divisible Markov processes $\{\xi^{{\epsilon}}_t\}_{0\leq t\leq T}$ with frequent small jumps depending on a small parameter $\epsilon>0,$ precise asymptotics for large deviations of integral…
We introduce and study new spectral invariant of two elliptic partial differential operators of Laplace and Dirac type on compact smooth manifolds without boundary that depends on both the eigenvalues and the eigensections of the operators,…
Additive processes are obtained from L\'{e}vy ones by relaxing the condition of stationary increments, hence they are spatially (but not temporally) homogeneous. By analogy with the case of time-homogeneous Markov processes, one can define…
We study the asymptotic stability of the semi-discrete (SD) numerical method for the approximation of stochastic differential equations. Recently, we examined the order of $\mathcal L^2$-convergence of the truncated SD method and showed…
We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process…
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification, are important because they are relatively easy to simulate. One does not…
We study the asymptotic behaviour of solutions of Forward Backward Stochastic Differential Equations in the coupled case, when the diffusion coefficient of the forward equation is multiplicatively perturbed by a small parameter that…
The asymptotic analysis of a class of stochastic partial differential equations (SPDEs) with fully locally monotone coefficients covering a large variety of physical systems, a wide class of quasilinear SPDEs and a good number of fluid…
Using Bellman function approach, we present new proofs of weighted $L^2$ inequalities for square functions, with the optimal dependence on the $A_2$ characteristics of the weight and further explicit constants. We study the estimates both…
We discuss the Donsker-Varadhan theory of large deviations in the framework of Hamiltonian systems thermostated by a Gaussian stochastic coupling. We derive a general formula for the Donsker-Varadhan large deviation functional for dynamics…
While small ball, or lower tail, asymptotic for Gaussian measures generated by solutions of stochastic ordinary differential equations is relatively well understood, a lot less is known in the case of stochastic partial differential…