相关论文: Pointwise eigenfunction estimates and intrinsic ul…

Consider the symmetric non-local Dirichlet form $(D,\D(D))$ given by $$ D(f,f)=\int_{\R^d}\int_{\R^d}\big(f(x)-f(y)\big)^2 J(x,y)\,dx\,dy $$with $\D(D)$ the closure of the set of $C^1$ functions on $\R^d$ with compact support under the norm…

Let $(X_t)_{t\ge 0}$ be a symmetric strong Markov process generated by non-local regular Dirichlet form $(D,\D(D))$ as follows \begin{equation*} \begin{split} & D(f,g)=\int_{\R^d}\int_{\R^d}\big(f(x)-f(y)\big)\big(g(x)-g(y)\big)…

We derive explicitly the coupling property for the transition semigroup of a L\'{e}vy process and gradient estimates for the associated semigroup of transition operators. This is based on the asymptotic behaviour of the symbol or the…

We study supercontractivity and hypercontractivity of Markov semigroups obtained via ground state transformation of non-local Schr\"odinger operators based on generators of symmetric jump-paring L\'evy processes with Kato-class confining…

We prove a version of the Feynman-Kac formula for Levy processes and integro-differential operators, with application to the momentum representation of suitable quantum (Euclidean) systems whose Hamiltonians involve L\'{e}vy-type…

We study the spatial decay of eigenfunctions of non-local Schr\"odinger operators whose kinetic terms are generators of symmetric jump-paring L\'evy processes with Kato-class potentials decaying at infinity. This class of processes has the…

Recently we extended the concept of intrinsic ultracontractivity to non-symmetric semigroups and proved that for a large class of non-symmetric diffusions Z with measure-valued drift and potential, the semigroup of Z^D (the process obtained…

We propose and study a certain discrete time counterpart of the classical Feynman--Kac semigroup with a confining potential in countable infinite spaces. For a class of long range Markov chains which satisfy the direct step property we…

The challenge to fruitfully merge state-of-the-art techniques from mathematical finance and numerical analysis has inspired researchers to develop fast deterministic option pricing methods. As a result, highly efficient algorithms to…

We study the long time asymptotics of probability density functions (pdfs) of L\'{e}vy flights in different confining potentials. For that we use two models: Langevin - driven and (L\'{e}vy - Schr\"odinger) semigroup - driven dynamics. It…

In this paper we first provide several conditional limit theorems for L\'evy processes with negative drift and regularly varying tail. Then we apply them to study the asymptotic behavior of expectations of some exponential functionals of…

The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…

We prove the intrinsic ultracontractivity for the semigroup generated by a large class of symmetric Levy processes such that the Levy measure satisfies some conditions in the neighborhood of 0, killed on exiting a bounded and connected…

In the first part of this paper, we give a useful criterion for uniform integrability of exponential martingales in the context of Markov processes. The condition of this criterion is easy to verify and is, in general, much weaker than the…

This paper generalizes the abstract method of proving an observability estimate by combining an uncertainty principle and a dissipation estimate. In these estimates we allow for a large class of growth/decay rates satisfying an…

Hypercontractivity of a quantum dynamical semigroup has strong implications for its convergence behavior and entropy decay rate. A logarithmic Sobolev inequality and the corresponding logarithmic Sobolev constant can be inferred from the…

For a (non-symmetric) strong Markov process $X$, consider the Feynman--Kac semigroup \[T_t^Af(x):=\mathbb {E}^x\bigl[e^{A_t}f(X_t)\bigr],\quad x\in {\mathbb {R}^n}, t>0,\] where $A$ is a continuous additive functional of $X$ associated with…

In this work, we investigate the compactness and the long time behavior of killed Feynman-Kac semigroups of various processes arising from statistical physics with very general singular Schr{\"o}dinger potentials. The processes we consider…

Strongly continuous semigroups of unital completely positive maps (i.e. quantum Markov semigroups or quantum dynamical semigroups) on compact quantum groups are studied. We show that quantum Markov semigroups on the universal or reduced…

We consider a class of L\'evy-type processes with unbounded coefficients, arising as Doob $h$-transforms of Feynman-Kac type representations of non-local Schr\"odinger operators, where the function $h$ is chosen to be the ground state of…