2016/06/17 by Paul-Éric Chaudru de Raynal, de Raynal, Paul-Eric Chaudru
Economics, Econometrics and Finance · Computer Science · Engineering · #Stochastic processes and financial applications #Advanced Mathematical Modeling in Engineering #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1606.05458
In this paper, we prove weak uniqueness of hypoelliptic stochastic differential equation with Hölder drift, with Hölder exponent strictly greater than 1/3. We then extend to a weak framework the previous work [CdR12] where strong uniqueness was proved when the Hölder exponent is strictly greater than 2/3. We also show that this result is sharp, by giving a counter example to weak uniqueness when the Hölder exponent is just below 1/3. Our approach is based on martingale problem formulation of Stroock and Varadhan and is based on smoothing properties of the associated PDE.