Related papers: Jump-type Hunt processes generated by lower bounde…
We consider a bivariate process $X_t=(X^1_t,X^2_t)$, which is observed on a finite time interval $[0,T]$ at discrete times $0,\Delta_n,2\Delta_n,....$ Assuming that its two components $X^1$ and $X^2$ have jumps on $[0,T]$, we derive tests…
This paper introduces test and estimation procedures for abrupt and gradual changes in the entire jump behaviour of a discretely observed Ito semimartingale. In contrast to existing work we analyse jumps of arbitrary size which are not…
We prove a robust super-hedging duality result for path-dependent options on assets with jumps, in a continuous time setting. It requires that the collection of martingale measures is rich enough and that the payoff function satisfies some…
The present paper continues the study of infinite dimensional calculus via regularization, started by C. Di Girolami and the second named author, introducing the notion of "weak Dirichlet process" in this context. Such a process $\X$,…
We consider a system of $N$ interacting particles, described by SDEs driven by Poisson random measures, where the coefficients depend on the empirical measure of the system. Every particle jumps with a jump rate depending on its position.…
The problem of drift estimation for the solution $X$ of a stochastic differential equation with L\'evy-type jumps is considered under discrete high-frequency observations with a growing observation window. An efficient and asymptotically…
For a continuous-time random walk $X=\{X_t,t\ge 0\}$ (in general non-Markov), we study the asymptotic behavior, as $t\rightarrow \infty$, of the normalized additive functional $c_t\int_0^{t} f(X_s)ds$, $t\ge 0$. Similarly to the Markov…
We study the homogenization for a class of non-symmetric pure jump Feller processes. The jump intensity involves periodic and aperiodic constituents, as well as oscillating and non-oscillating constituents. This means that the noise can…
In this paper, we first extend the approximate factorization for purely discontinuous Markov process established in \cite{CKSV20} by getting rid of some of the conditions imposed in \cite{CKSV20}. Then we apply the approximate factorization…
Let $X$ be an isotropic unimodal L\'{e}vy jump process on $\mathbb{R}^d$. We develop probabilistic methods which in many cases allow us to determine whether $X$ satisfies the elliptic Harnack inequality (EHI), by looking only at the jump…
This paper is concerned with reconstruction issue of inverse obstacle problems governed by partial differential equations and consists of two parts. (i) The first part considers the foundation of the probe and enclosure methods for an…
This work provides a semi-analytic approximation method for decoupled forwardbackward SDEs (FBSDEs) with jumps. In particular, we construct an asymptotic expansion method for FBSDEs driven by the random Poisson measures with {\sigma}-finite…
The cooperative dynamics of a 1-D collection of Markov jump, interacting stochastic processes is studied via a mean-field approach. In the time-asymptotic regime, the resulting nonlinear master equation is analytically solved. The…
In this article, we deal with stochastic horizontal lifts and anti-developments of semimartingales with jumps on complete and connected Riemannian manifolds without any assumption for their curvatures. We prove two one-to-one…
The fractional Laplacian $(- \Delta)^{\alpha /2}$, $\alpha \in (0,2)$ has many equivalent (albeit formally different) realizations as a nonlocal generator of a family of $\alpha $-stable stochastic processes in $R^n$. On the other hand, if…
In this paper, we consider a diffusion process with jumps whose drift and jump coefficient depend on an unknown parameter. We then give a self-contained proof of the local asymptotic mixed normality (LAMN) property when the process is…
We show that for ultracontractive irreducible Dirichlet metric measure spaces, the Dirichlet spectrum is discrete for a restriction to any connected open set without any assumption on regularity of the boundary. The main applications…
Standard methods for detecting discontinuities in conditional means are not applicable to outcomes that are complex, non-Euclidean objects like distributions, networks, or covariance matrices. This article develops a nonparametric test for…
We consider partial exclusion processes~(PEPs) on the one-dimensional square lattice, that is, a system of interacting particles where each particle random walks according to a jump rate satisfying an exclusion rule that allows up to a…
In this paper, we study formal synthesis of control policies for partially observed jump-diffusion systems against complex logic specifications. Given a state estimator, we utilize a discretization-free approach for formal synthesis of…