Statistical analysis of tempo-spatial stochastic integral processes

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In the renewal time of the project, we want to derive new nonparametric estimation methods for parabolic SPDEs with a Gaussian driving noise exhibiting a spatial covariance that is smoother than the Riesz kernels considered in the original project. This is motivated from financial mathematics, where one is concerned with modeling term structure dynamics of forward rates with the objective of pricing interest rate derivative securities. Empirical observations suggest that fluctuations of the term structure should be smooth in the time to maturity while irregular in time. Based on high-frequency data, we want to construct consistent and asymptotically normal estimators for stochastic volatility (and the spatial noise correlation index) by proving limit theorems for the normalized power variations of the stochastic heat equation in this new setting.