Explicit local density bounds for Itô-processes with irregular drift

2023/08/04 by Krühner, Paul, Xu, Shijie
#49N60 #60H10 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2308.02241

Abstract

We find explicit upper bounds for the density of marginals of continuous diffusions where we assume that the diffusion coefficient is constant and the drift is solely assumed to be progressively measurable and locally bounded. In one dimension we extend our result to the case that the diffusion coefficient is a locally Lipschitz-continuous function of the state. Our approach is based on a comparison to a suitable doubly reflected Brownian motion whose density is known in a series representation.

Related

• A sharp upper bound for the expected occupation density of Itô processes with bounded irregular drift and diffusion coefficients
• Local densities for a class of degenerate diffusions
• On the first time that an Ito process hits a barrier
• Exponential bounds for the density of the law of the solution of a SDE with locally Lipschitz coefficients
• On potentials of Itô's processes with drift in L_d+1