相关论文: A New Approach to Inverse Local Times

We derive a Ray-Knight type theorem for the local time process (in the space variable) of a skew Brownian motion up to an independent exponential time. It is known that the local time seen as a density of the occupation measure and taken…

We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-dimensional reflecting diffusions whose noise is a function…

Inverse scattering and spectral one-dimensional problems are discussed systematically in a self-contained way. Many novel results, due to the author are presented. The classical results are often presented in a new way. Several highlights…

Owing to the Rosenau argument in Physical Review A, 46 (1992), pag. 12-15, originally proposed to obtain a regularized version of the Chapman-Enskog expansion of hydrodynamics, we introduce a non-local linear kinetic equation which…

In this paper, we study the law of the local time processes $(L_T^x(X),x\in \mathbb{R})$ associated to a spectrally negative L\'evy process $X$, in the cases $T=\tau_a^+$, the first passage time of $X$ above $a>0$ and $T=\tau(c)$, the first…

A detailed discussion of the Krein's results (applicable for solving the inverse scattering problem) is given with complete proofs.

This is a comment on [G. Knight and R. Klages, Phys. Rev. E 84, 041135 (2011); also available at arXiv:1107.5293v2 [math-ph]].

We give a new proof for a Ray-Knight representation of Feller's branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion $H$ with a drift that is affine linear in the local time accumulated by $H$…

In this paper, we study inverse local time at 0 of one-dimensional reflected diffusions on $[0, \infty)$, and establish a comparison principle for inverse local times. Applications to Green function estimates for non-local operators are…

This is a revision of my original posting, in which I raised objections to part of the Conway-Kochen argument. I now agree with them that their recent reply answers my original concerns. In the first part of these notes (identical to the…

We present a simple stochastic integral representation for the local times of the height process of a spectrally positive Levy process stopped at a hitting time. From the representation we derive a strong stochastic equation for the local…

A reference potential approach to the one-dimensional quantum-mechanical inverse problem is developed. All spectral characteristics of the system, including its discrete energy spectrum, the full energy dependence of the phase shift, and…

We apply the shifted composition rule -- an information-theoretic principle introduced in our earlier work [AC23] -- to establish shift Harnack inequalities for the Langevin diffusion. We obtain sharp constants for these inequalities for…

Diffraction is a phenomenon, discussed for centuries from various points of view. The very simple principle, proposed by Huygens [1] and then modified by Fresnel[2], Stokes [3] and Kirchoff [4], allows us to make calculations, substituting…

We proceed here with our systematic study, initiated in [3], of multiscale problems with defects, within the context of homogenization theory. The case under consideration here is that of a diffusion equation with a diffusion coefficient of…

This paper investigates an inverse source problem for space-time fractional diffusion equations from a posteriori interior measurements. The uniqueness result is established by the memory effect of fractional derivatives and the unique…

The concept of spectral relative entropy rate is introduced for jointly stationary Gaussian processes. Using classical information-theoretic results, we establish a remarkable connection between time and spectral domain relative entropy…

The inversion of a Levy measure was first introduced (under a different name) in Sato 2007. We generalize the definition and give some properties. We then use inversions to derive a relationship between weak convergence of a Levy process to…

This article presents a finite element scheme with Newton's method for solving the time-fractional nonlinear diffusion equation. For time discretization, we use the fractional Crank-Nicolson scheme based on backward Euler convolution…

The goal of this overview article is to give a tangible presentation of recent breakthrough works in discrepancy theory by M. B. Levin. These works provide proofs for the exact lower discrepancy bounds of Halton's sequence and a certain…