2023/09/12 by Liping Li, Ying Li, Li, Liping +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Diffusion and Search Dynamics #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2309.06211
openalex publication_date 2023/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quasidiffusion is an extension of regular diffusion which can be described as a Feller process on ℝ with infinitesimal operator L=(1)/(2)DmDs. Here, s(x) = x and m refers to the (not necessarily fully supported) speed measure. In this paper, we will examine an analogous operator where the scale function s is general and only assumed to be non-decreasing. We find that, like regular diffusion or quasidiffusion, the reproducing kernel can still be generated by two specific positive monotone solutions of the α-harmonic equation Lf = αf for each α>0. Our main result shows that this reproducing kernel is able to induce a Markov process, which is identical to that obtained in [25] using a semigroup approach or in [17] through Dirichlet forms. Further investigations into the properties of this process will be presented.