4 problems

Let $H\in(0,1)$ be the Hurst parameter of fractional Brownian motion, and let $\gamma$ denote the Hölder regularity exponent of the coefficient $\sigma$. Pathwise uniqueness failur…

Let $H\in[1,\infty)\setminus\mathbb{N}$ be the Hurst parameter of fractional Brownian motion, and let $\gamma$ denote the Hölder regularity exponent of the coefficient $\sigma$. Th…

Consider a competing particle system with $n\geq 3$ particles, and let $X(\cdot)$ denote its particle process. A solution is strong when it is adapted to the driving noise, and pat…

Consider the stochastic heat equation … alpha<2(2gamma-1), … . This strengthens the preceding pathwise-uniqueness result in the white-noise case, where the argument gives the condi…