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Consider a stationary Gaussian random field on R d with spectral density f (λ) that satisfies f (λ) ∼ c |λ| −θ as |λ| → ∞. The parameters c and θ control the tail behavior of the spectral density. c is related to a microergodic parameter and θ is related to a fractal index. For data observed on a grid, we propose estimators of c and θ by minimizing an… (More)

Consider a stationary Gaussian random field on R d with the spectral density f (λ) that satisfies f (λ) ∼ c |Hλ| −θ as |λ| → ∞ for some nonsingular matrix H. The parameters c and θ control the tail behavior of the spectral density. c is related to a microergodic parameter and θ is related to a fractal index. For data observed on a grid, we propose… (More)

- Hassan Allouba, Yimin Xiao
- 2016

We establish exact, dimension-dependent, spatio-temporal, uniform and local moduli of continuity for (1) the fourth order L-Kuramoto-Sivashinsky (L-KS) SPDEs and for (2) the time-fractional stochastic partial integro-differential equations (SPIDEs), driven by space-time white noise in one-to-three dimensional space. Both classes were introduced—with… (More)

We show that for a wide class of Gaussian random fields, points are polar in the critical dimension. Examples of such random fields include solutions of systems of linear stochastic partial differential equations with deterministic coefficients, such as the stochastic heat equation or wave equation with space-time white noise, or colored noise in spatial… (More)

- Tom Conner, Artem Prokhorov, Connie Page, Yu Fang, Yimin Xiao, Lori A Post
- Journal of interpersonal violence
- 2011

Elder abuse in long-term care has become a very important public health concern. Recent estimates of elder abuse prevalence are in the range of 2% to 10% (Lachs & Pillemer, 2004), and current changes in population structure indicate a potential for an upward trend in prevalence (Malley-Morrison, Nolido, & Chawla, 2006; Post et al., 2006). More than 20 years… (More)

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