9 problems

Universality conjecture. For an arbitrary Hubbard–Stratonovich factorization of this form, the quantity $DG$ is always given by the matrix displayed in equation (3.63) of the sourc…

Let $W$ be a Brownian motion and let $\bar{\bm{\lambda}}$ be an extension of Lebesgue measure arising from a rich Fubini extension, under which a process with the weaker measurabil…

The results concern paths with finite $p$-th variation along a sequence of time partitions, including pathwise change-of-variable formulas, compensated Riemann sums, and path-depen…

Ayed–Kuo insider-trading solution conjecture. The solution is

Extension conjecture. Theorem should extend to cover this new class of functions $\sigma(x)$.

Let $B$ be fractional Brownian motion, and let ${\bf B}=({\bf B}^1_{ts},\ldots,{\bf B}^N_{ts})$ be one of the Hölder-continuous rough paths over $B$ constructed by Fourier normal o…

A $g$-martingale is a martingale arising from a filtration-consistent nonlinear expectation defined via a backward stochastic differential equation, while a $G$-martingale is the c…

Bounded-variation extension conjecture. The results of the paper hold when $\xi$ is only required to be of bounded variation. This would extend the stochastic integral construction…

A stochastic process with fourth-order scaling properties is a process whose increments contribute at fourth order under the relevant scaling, as in a process with nontrivial quart…