On diffusion processes with drift in L_d+1

2021/02/23 by N. V. Krylov, Krylov, N. V.
Economics, Econometrics and Finance · Mathematics · #60H10 #60J60 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2102.11465

openalex publication_date 2021/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a natural continuation of \citeKr₂0₂ and \citeKr₂1₁ where strong Markov processes are constructed in time inhomogeneous setting with Borel measurable uniformly bounded and uniformly nondegenerate diffusion and drift in L_d+1(ℝ^d+1) and some properties of their Green's functions and probability of passing through narrow tubes are investigated. On the basis of this here we study some further properties of these processes such as Harnack inequality, Hölder continuity of potentials, Fanghua Lin estimates and so on.

Related

• On potentials of Itô's processes with drift in L_d+1
• Some properties of solutions of Itô equations with drift in L_d+1
• On diffusion processes with drift in a Morrey class containing L_d+2
• On diffusion processes with drift in L_d
• A note on the strong Feller property of diffusion processes