Establishes optimal local well-posedness for reaction-diffusion SPDEs with non-trace-class multiplicative noise, critical initial-data spaces, instantaneous regularization, and applications to prototypical models.
Stochastic Volterra Equations in Banach Spac es and Stochastic Partial Differential Equation
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Develops a Hilbert space-valued Markovian lift framework for stochastic Volterra equations and establishes existence of limit distributions, LLN with convergence rate, and CLT for time averages in the Gaussian domain.
Constructs QMLE for drift parameter in singular Volterra SDE with small diffusion, proving path reconstruction error O(h^{1/2}) independent of roughness α and yielding efficient estimator as ε→0.
Constructs a consistent and asymptotically normal trajectory fitting estimator for the drift parameter θ* in singular-kernel stochastic Volterra equations under small-noise asymptotics.
citing papers explorer
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An optimal local theory for reaction-diffusion equations driven by non-trace-class noise
Establishes optimal local well-posedness for reaction-diffusion SPDEs with non-trace-class multiplicative noise, critical initial-data spaces, instantaneous regularization, and applications to prototypical models.
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Limit theorems for stochastic Volterra processes
Develops a Hilbert space-valued Markovian lift framework for stochastic Volterra equations and establishes existence of limit distributions, LLN with convergence rate, and CLT for time averages in the Gaussian domain.
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Drift estimation for rough processes under small noise asymptotic : QMLE approach
Constructs QMLE for drift parameter in singular Volterra SDE with small diffusion, proving path reconstruction error O(h^{1/2}) independent of roughness α and yielding efficient estimator as ε→0.
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Drift estimation for rough processes under small noise asymptotic : trajectory fitting method
Constructs a consistent and asymptotically normal trajectory fitting estimator for the drift parameter θ* in singular-kernel stochastic Volterra equations under small-noise asymptotics.