Temporal quartic variation for non-linear stochastic heat equations with piecewise constant coefficients
arXiv:2410.22750
summary
The paper studies a stochastic heat equation with piecewise constant coefficients driven by multiplicative space‑time white noise, proving existence and uniqueness of its mild solution and analyzing the limit behavior of its temporal quartic variation, which leads to a consistent estimator.
Abstract
We consider a stochastic partial differential equation with piecewise constant coefficients driven by a multiplicative space-time white noise. The existence and uniqueness of the mild solution in Walsh sense is established. We mainly study the limit behavior of the temporal quartic variation of the mild solution. As an application, we deduce a consistent estimator based on corresponding results.
Topics & keywords
#stochastic partial differential equations#stochastic heat equation#multiplicative noise#quartic variation#piecewise constant coefficients#parameter estimationmild solutionWalsh integralspace-time white noisetemporal quartic variationconsistent estimator