Related papers: Pathwise differentiability of reflected diffusions…
Recently, rectified flow (RF)-based models have achieved state-of-the-art performance in many areas for both the multi-step and one-step generation. However, only a few theoretical works analyze the discretization complexity of RF-based…
Fourth-order accurate compact schemes for variable coefficient convection diffusion equations are considered. A sufficient condition for the stability of the fully discrete problem is derived using a difference equation based approach. The…
A theoretical analysis of the statistical distributions of the reflected intensities from random media is presented. We use random matrix theory to analytically deduce the probability densities in the localization regime. Numerical…
We study the regularity of a diffusion on a simplex with singular drift and reflecting boundary condition which describes a finite system of particles on an interval with Coulomb interaction and reflection between nearest neighbors. As our…
The concept of the derivative-dependent functional separable solution, as a generalization to the functional separable solution, is proposed. As an application, it is used to discuss the generalized nonlinear diffusion equations based on…
We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec…
A new proof of a pathwise uniqueness result of Krylov and R\"{o}ckner is given. It concerns SDEs with drift having only certain integrability properties. In spite of the poor regularity of the drift, pathwise continuous dependence on…
Some topological properties of stochastic flow $\varphi_t(x)$ generated by stochastic differential equation in a ${\mathbb R}^d_+$ with normal reflection at the boundary are investigated. Sobolev differentiability in initial condition is…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
We study a general limiting framework for the convergence of sequences of additive functionals of diffusions to L\'evy subordinators, and provide explicit sufficient conditions that both ensure convergence and characterize the law of the…
This PhD thesis studies the broken ray transform, a generalization of the geodesic X-ray transform where geodesics are replaced with broken rays that reflect on a part of the boundary. The fundamental question is whether this transform is…
This paper describes the use of Feynman photon path integrals to compute the probability of detecting reflected, diffracted, and scattered photons at different points in space after interacting with conduction electrons. Five examples are…
Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as point-like objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this…
We establish the existence of solutions to path-dependent rough differential equations with non-anticipative coefficients. Regularity assumptions on the coefficients are formulated in terms of horizontal and vertical derivatives.
The Markov chain approximation of a one-dimensional symmetric diffusion is investigated in this paper. Given an irreducible reflecting diffusion on a closed interval with scale function $s$ and speed measure $m$, the approximating Markov…
We consider inference of the parameters of the diffusion term for Cox-Ingersoll-Ross and similar processes with a power type dependence of the diffusion coefficient from the underlying process. We suggest some original pathwise estimates…
Reaction-diffusion models have been used over decades to study biological systems. In this context, evolution equations for probability distribution functions and the associated stochastic differential equations have nowadays become…
In this paper we investigate deterministic diffusion in systems which are spatially extended in certain directions but are restricted in size and open in other directions, consequently particles can escape. We introduce besides the…
The radiation (reaction, Robin) boundary condition for the continuum diffusion equation is widely used in chemical and biological applications to express reactive boundaries. The underlying trajectories of the diffusing particles are…
In this paper, we consider directed polymers in random environment with discrete space and time. For transverse dimension at least equal to 3, we prove that diffusivity holds for the path in the full weak disorder region, i.e., where the…