{
  "id": "1802.01829",
  "version": "v1",
  "published": "2018-02-06T07:41:05.000Z",
  "updated": "2018-02-06T07:41:05.000Z",
  "title": "Average Case $(s, t)$-weak tractability of non-homogenous tensor product problems",
  "authors": [
    "Jia Chen",
    "Heping Wang",
    "Jie Zhang"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NA"
  ],
  "abstract": "We study $d$-variate problem in the average case setting with respect to a zero-mean Gaussian measure. The covariance kernel of this Gaussian measure is a product of univariate kernels and satisfies some special properties. We study $(s, t)$-weak tractability of this multivariate problem, and obtain a necessary and sufficient condition for $s>0$ and $t\\in(0,1)$. Our result can apply to the problems with covariance kernels corresponding to Euler and Wiener integrated processes, Korobov kernels, and analytic Korobov kernels.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-02-06T07:41:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A25",
      "41A63",
      "65D15",
      "65Y20"
    ],
    "keywords": [
      "non-homogenous tensor product problems",
      "weak tractability",
      "average case",
      "covariance kernel",
      "analytic korobov kernels"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}