Related papers: Heat kernel of fractional Laplacian in cones
We consider a spectrally negative branching L{\'e}vy process where the particles undergo dyadic branching and are killed when entering the negative half-plane. The purpose of this short note is to give conditions under which this process…
In this paper, sharp two-sided estimates for the transition densities of relativistic $\alpha$-stable processes with mass $m\in (0, 1]$ in $C^{1,1}$ exterior open sets are established for all time $t>0$. These transition densities are also…
Quenched and annealed heat kernel estimates are established for Fontes-Isopi-Newman (FIN) processes on spaces equipped with a resistance form. These results are new even in the case of the one-dimensional FIN diffusion, and also apply to…
Taking account of recent developments in the representation of $d$-dimensional isotropic stable L\'evy processes as self-similar Markov processes, we consider a number of new ways to condition its path. Suppose that $\Omega$ is a region of…
We study a spatial asymptotic behaviour at infinity of kernels $p_t(x)$ for convolution semigroups of nonlocal pseudo-differential operators. We give general and sharp sufficient conditions under which the limits $$ \lim_{r \to \infty}…
A new algebraic approach for calculating the heat kernel for the Laplace operator on any Riemannian manifold with covariantly constant curvature is proposed. It is shown that the heat kernel operator can be obtained by an averaging over the…
Suppose that $\mathsf{S}$ is a closed set of the unit sphere $\mathbb{S}^{d-1} = \{x\in \mathbb{R}^d: |x| =1\}$ in dimension $d\geq2$, which has positive surface measure. We construct the law of absorption of an isotropic stable L\'evy…
Motivated by classical considerations from risk theory, we investigate boundary crossing problems for refracted L\'evy processes. The latter is a L\'evy process whose dynamics change by subtracting off a fixed linear drift (of suitable…
In this paper, we establish existence and uniqueness of weak solutions to general time fractional equations and give their probabilistic representations. We then derive sharp two-sided estimates for fundamental solutions of a family of time…
Let $d \geq 2$, $\alpha \in (0,2)$, and $X$ be the rectilinear $\alpha$-stable process on $\mathbb{R}^d$. We first present a geometric characterization of an open subset $D\subset \mathbb{R}^d$ so that the part process $X^D$ of $X$ in $D$…
We prove universality of the Yaglom limit of Lipschitz cones among all unimodal L\'{e}vy processes sufficiently close to the isotropic $\alpha$-stable L\'{e}vy process.
For $d\geq 1$ and $0<\beta<\alpha<2$, consider a family of pseudo differential operators $\{\Delta^{\alpha} + a^\beta \Delta^{\beta/2}; a \in [0, 1]\}$ that evolves continuously from $\Delta^{\alpha/2}$ to $ \Delta^{\alpha/2}+…
In this paper we solve the exit problems for (reflected) spectrally negative L\'evy processes, which are exponentially killed with a killing intensity dependent on the present state of the process and analyze respective resolvents. All…
We prove that on an asymptotically Euclidean boundary groupoid, the heat kernel of the Laplacian is a smooth groupoid pseudo-differential operator.
We prove heat kernel estimates for the $\bar\partial$-Neumann Laplacian acting in spaces of differential forms over noncompact, strongly pseudoconvex complex manifolds with a Lie group symmetry and compact quotient. We also relate our…
Methods of extraction of the symmetry energy (or enthalpy) coefficient to temperature ratio from isobaric and isotopic yields of fragments produced in Fermi-energy heavy-ion collisions are discussed. We show that the methods are consistent…
We consider the class of (possibly killed) spectrally positive L\'evy process that have been time-changed by the inverse of an integral functional. Within this class we characterize the family of those processes which satisfy the following…
The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different L\'evy processes: in the first model we…
The isotropic 4-wave kinetic equation is considered in its weak formulation using model (simplified) homogeneous kernels. Existence and uniqueness of solutions is proven in a particular setting where the kernels have a rate of growth at…
In contrast to their seemingly simple and shared structure of independence and stationarity, L\'evy processes exhibit a wide variety of behaviors, from the self-similar Wiener process to piecewise-constant compound Poisson processes.…