Degenerate SDE with Hölder-Dini Drift and Non-Lipschitz Noise Coefficient

2015/04/17 by Feng‐Yu Wang, Xicheng Zhang, Wang, Feng-Yu +1 · 3 citations
Computer Science · Economics, Econometrics and Finance · #FOS: Mathematics #Financial Risk and Volatility Modeling #Image and Signal Denoising Methods #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1504.04450

openalex publication_date 2015/04/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The existence-uniqueness and stability of strong solutions are proved for a class of degenerate stochastic differential equations, where the noise coeffcicient might be non-Lipschitz, and the drift is locally Dini continuous in the component with noise (i.e. the second component) and locally Hölder-Dini continuous of order \ff 2 3 in the first component. Moreover, the weak uniqueness is proved under weaker conditions on the noise coefficient. Furthermore, if the noise coefficient is C^1+\vv for some \vv>0 and the drift is Hölder continuous of order å∈ (\ff 2 3,1) in the first component and order \bb∈(0,1) in the second, the solution forms a C¹-stochastic diffeormorphism flow. To prove these results, we present some new characterizations of Hölder-Dini space by using the heat semigroup and slowly varying functions.

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