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We study the quadratic variations (in time and in space) of the solution to the stochastic wave equation driven by the space-time white noise. We give their limit (almost surely and in L 2 (Ω)) and we prove that these variations satisfy, after a proper renormalization, a Central Limit Theorem. We apply the quadratic variation to define and analyze estimators for the drift parameter of the wave equation. [ABSTRACT FROM AUTHOR]

We consider the sequence of spatial quadratic variations of the solution to the stochastic heat equation with space-time white noise. This sequence satisfies a Central Limit Theorem. By using Malliavin calculus, we refine this result by proving the convergence of the sequence of densities and by finding the second-order term in the asymptotic expansion of the densities. In particular, our proofs are based on sharp estimates of the correlation structure of the solution, which may have their own interest. [ABSTRACT FROM AUTHOR]

Let be the solution to the linear stochastic heat equation driven by a fractional noise in time with correlated spatial structure. We study various path properties of the process with respect to the time and to the space variable, respectively. In particular, we derive exact uniform moduli of continuity and Chung-type laws of iterated logarithm. [ABSTRACT FROM AUTHOR]

We consider the solution to the stochastic heat equation driven by the time-space white noise and study the asymptotic behavior of its spatial quadratic variations with 'moving time', meaning that the time variable is not fixed and its values are allowed to be very big or very small. We investigate the limit distribution of these variations via Malliavin calculus. [ABSTRACT FROM AUTHOR]

We study the asymptotic behavior of the aggregated fractional Ornstein-Uhlenbeck processes with random coefficients that follows a Gamma-type distribution. We also analyze the properties of the limit process. [ABSTRACT FROM AUTHOR]

We prove central and non-central limit theorems for the Hermite variations of the anisotropic fractional Brownian sheet Wα, β with Hurst parameter (α, β) ∈ (0, 1)2. When $0 \lt \alpha \leq 1-\frac{1}{2q}$ or $0 \lt \beta \leq 1-\frac{1}{2q}$ a central limit theorem holds for the renormalized Hermite variations of order q ≥ 2, while for $1-\frac{1}{2q} \lt \alpha, \beta \lt 1$ we prove that these variations satisfy a non-central limit theorem. In fact, they converge to a random variable which is the value of a two-parameter Hermite process at time (1, 1). [ABSTRACT FROM AUTHOR]

Using the Malliavin calculus with respect to Gaussian processes and the multiple stochastic integrals, we derive Itô's and Tanaka's formulas for the d-dimensional bifractional Brownian motion. [ABSTRACT FROM AUTHOR]