Parameter Estimates and Exact Variations for Stochastic Heat Equations Driven by Space-Time White Noise

Abstract

In this article we calculate the exact quadratic variation in space and quartic variation in time for the solutions to a one dimensional stochastic heat equation driven by a multiplicative space-time white noise. We use the knowledge of exact variations to estimate the drift parameter appearing in the equation.

Keywords:

• Anderson model
• Edwards–Wilkinson model
• Gaussian processes
• Parameter estimates
• Path variations
• Space-time white noise
• Stochastic partial differential equations

2000 Mathematics Subject Classification:

• 60G15
• 60H10
• 60H30

This work was partially supported by the GACR Grant 201/04/0750 and by the MSMT Research Plan MSM 4977751301