- Date: 19 April (Thu.) 16:30 — 18:00
- Place: W.W. 7th-floor
- Speaker: Go Yuki
- Title: Local and Global H\”older Properties of the Density of the Solutions of SDEs with Singular Coefficients
- Abstract:
Consider a uniformly elliptic one dimensional stochastic differential equation with locally smooth diffusion coefficient and H\”older continuous drift.
We prove that the density of the solution locally exists and is H\”older continuous.
In concrete terms, if the diffusion coefficient is infinitely differentiable and the drift is $\alpha$-H\”older continuous on some interval then for any $\gamma\in(0,\alpha)$the density is $\gamma$-H\”older continuous on this set.
Hence the drift may be a determining factor in the H\”older continuity of the density.
Also we prove the existence and global H\”older continuity of the density of the weak solution of a d-dimensional SDE with bounded deterministic diffusion coefficient, bounded drift and compound Poisson process.
In this case, we assume that the Fourier transform of the drift exists.
In the proof, we treat the integrability of the Fourier transform of the drift instead of a H\”older continuity of the drift in the local case.
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