Variance inequalities for covariance kernels and applications to central limit theorems

Exponential inequalities and functional central limit theorems for random fields

We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform...

Bounds for the covariance of functions of infinite variance stable random variables with applications to central limit theorems and wavelet-based estimation

VLADAS PIPIRAS, MURAD S. TAQQU and PATRICE ABRY Department of Statistics and Operations Research, UNC-CH, CB #3260, Chapel Hill, NC 27599-3260, USA. E-mail: [email protected] Department of Mathematics and Statistics, Boston University, 111 Cummington St., Boston, MA 02215, USA. E-mail: [email protected] CNRS UMR 5672, Ecole Normale Supérieure de Lyon, Laboratoire de Physique, 69 364 Lyon Ce...

Small Time Central Limit Theorems for Semimartingales with Applications

We give conditions under which the normalized marginal distribution of a semimartingale converges to a Gaussian limit law as time tends to zero. In particular, our result is applicable to solutions of stochastic differential equations with locally bounded and continuous coefficients. The limit theorems are subsequently extended to functional central limit theorems on the process level. We prese...

Applications of Central Limit Theorems for Equity-linked Insurance

In both the past literature and industrial practice, it was often implicitly used without any justification that the classical strong law of large numbers applies to the modeling of equitylinked insurance. However, as all policyholders’ benefits are linked to common equity indices or funds, the classical assumption of independent claims is clearly inappropriate for equity-linked insurance. In o...

When Bias Kills the Variance: Central Limit Theorems for DEA and FDH Efficiency Scores: Technical Appendix