A Random Change of Variables and Applications to the Stochastic Porous Medium Equation with Multiplicative Time Noise

A change of variables is introduced to reduce certain nonlinear stochastic evolution equations with multiplicative noise to the corresponding deterministic equation. The result is then used to investigate a stochastic porous medium equation

A Sharp Rate of Convergence in the Functional Central Limit Theorem with Gaussian Input

When the underlying random variables are Gaussian, the classical Central Limit Theorem (CLT) is trivial, but the functional CLT is not. The objective of the paper is to investigate the functional CLT for stationary Gaussian processes in the Wasserstein-1 metric on the space of continuous functions. Matching upper and lower bounds are established, indicating that the convergence rate is slightly faster than in the L\'{e}vy-Prokhorov metric

A Note on Generalized Malliavin Calculus

The Malliavin derivative, divergence operator, and the Ornstein-Uhlenbeck operator are extended from the traditional Gaussian setting to generalized processes from the higher-order chaos spaces