相关论文: Interior Schauder estimates for elliptic equations…

We are interested in some properties related to the solutions of non-local diffusion equations with divergence free drift. Existence, maximum principle and a positivity principle are proved. In order to study Holder regularity, we apply a…

Given $n$ equidistant realisations of a L\'evy process $(L_t,\,t\ge 0)$, a natural estimator $\hat N_n$ for the distribution function $N$ of the L\'evy measure is constructed. Under a polynomial decay restriction on the characteristic…

Consider the following stochastic differential equation for $(X_t)_{t\ge 0}$ on $\mathbb R^d$ and its Euler-Maruyama (EM) approximation $(Y_{t_n})_{n\in \mathbb Z^+}$: \begin{align*} &d X_t=b( X_t) d t+\sigma(X_t) d B_t, \\ &…

Using heat kernel estimates, we prove the pathwise uniqueness for strong solutions of irregular stochastic differential equation driven by a family of Markov process, whose generator is a non-local and non-symmetric L\'evy type operator.…

In this work, we propose and analyze a pointwise a posteriori error estimator for simple eigenvalues of elliptic eigenvalue problems with adaptive finite element methods (AFEMs). We prove the reliability and efficiency of the residual-type…

These are the notes of a part of the PhD course Regularity for free boundary problems and for elliptic PDEs, held in Pavia in the spring of 2025. The aim is to provide a comprehensive and self-contained treatment of classical interior and…

We construct an efficient integrator for stochastic differential systems driven by Levy processes. An efficient integrator is a strong approximation that is more accurate than the corresponding stochastic Taylor approximation, to all orders…

In this manuscript, we derive Schauder estimates for viscosity solutions to non-convex fully nonlinear second-order parabolic equations \[ \partial_t u - F(x, t,D^2u) = f (x, t) \quad \text{in} \quad \mathrm{Q}_1 = B_1 \times (-1, 0], \]…

This paper explicitly computes the transition densities of a spectrally negative stable process with index greater than one, reflected at its infimum. First we derive the forward equation using the theory of sun-dual semigroups. The…

In this paper we first study the generalized weighted Hardy spaces $H^p_{L,w}(X)$ for $0<p\le 1$ associated to nonnegative self-adjoint operators $L$ satisfying Gaussian upper bounds on the space of homogeneous type $X$ in both cases of…

In this paper we develop a new method based on Littlewood-Paley's decomposition and heat kernel estimates of integral form, to establish Schauder's estimate for the following degenerate nonlocal equation in $\mathbb R^{2d}$ with H\"older…

We present a general blow-up technique to obtain local regularity estimates for solutions, and their derivatives, of second order elliptic equations in divergence form in H\"older spaces with variable exponent. The procedure allows to…

We consider solutions of L\'evy-driven stochastic differential equations of the form $\mathrm{d} X_t=\sigma(X_{t-})\mathrm{d} L_t$, $X_0=x$ where the function $\sigma$ is twice continuously differentiable and maximal of linear growth and…

We study local regularity properties of local minimizer of scalar integral functionals of the form $$\mathcal F[u]:=\int_\Omega F(\nabla u)-f u\,dx$$ where the convex integrand $F$ satisfies controlled $(p,q)$-growth conditions. We…

We consider a class of {energy integrals}, associated to nonlinear and non-uniformly elliptic equations, with integrands $f(x,u,\xi)$ satisfying anisotropic $p_i,q$-growth conditions of the form $$ \sum_{i=1}^n \lambda_i (x)|\xi_i|^{p_i}\le…

Given a low frequency sample of an infinitely divisible moving average random field $\{\int_{\mathbb{R}^d} f(x-t)\Lambda(dx); \ t \in \mathbb{R}^d \}$ with a known simple function $f$, we study the problem of nonparametric estimation of the…

The aim of this paper is to study the laws of the exponential functionals of the processes $X$ with independent increments, namely $$I_t= \int _0^t\exp(-X_s)ds, \,\, t\geq 0,$$ and also $$I_{\infty}= \int _0^{\infty}\exp(-X_s)ds.$$ Under…

We consider high frequency samples from ergodic L\'evy driven stochastic differential equation (SDE) with drift coefficient $a(x,\alpha)$ and scale coefficient $c(x,\gamma)$ involving unknown parameters $\alpha$ and $\gamma$. We suppose…

We obtain series expansions of the $q$-scale functions of arbitrary spectrally negative L\'evy processes, including processes with infinite jump activity, and use these to derive various new examples of explicit $q$-scale functions.…

In this paper, we are concerned with the estimates for the moments of stochastic convolution integrals. We first deal with the stochastic singular integral operators and we aim to derive the Morrey-Campanato estimates for the $p$-moments…