{
  "id": "1101.5515",
  "version": "v3",
  "published": "2011-01-28T11:42:19.000Z",
  "updated": "2017-08-23T21:52:40.000Z",
  "title": "Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales",
  "authors": [
    "Arnab Ganguly"
  ],
  "comment": "47 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The paper concerns itself with establishing large deviation principles for a sequence of stochastic integrals and stochastic differential equations driven by general semimartingales in infinite-dimensional settings. The class of semimartingales considered is broad enough to cover Banach space-valued semimartingales and the martingale random measures. Simple usable expressions for the associated rate functions are given in this abstract setup. As illustrated through several concrete examples, the results presented here provide a new systematic approach to the study of large deviation principles for a sequence of Markov processes. Keywords: large deviations, stochastic integration, stochastic differential equations, exponential tightness, Markov processes, infinite dimensional semimartingales, Banach space-valued semimartingales",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-07-12T10:43:51.000Z",
      "abstract": "The paper deals with the large deviation principle for a sequence of stochastic integrals and stochastic differential equations in infinite-dimensional settings. Let $\\H$ be a separable Banach space. We consider a sequence of stochastic integrals $\\{X_{n-}\\cdot Y_n\\}$, where $\\{Y_n\\}$ is a sequence of infinite-dimensional semimartingales indexed by $\\H\\times [0,\\infty)$ and the $X_n$ are $\\H$-valued cadlag processes. Assuming that $\\{(X_n,Y_n)\\}$ satisfies a large deviation principle, a uniform exponential tightness condition is described under which a large deviation principle holds for $\\{(X_n,Y_n,X_{n-}\\cdot Y_n)\\}$. An expression for the rate function of the sequence of stochastic integrals $\\{X_{n-}\\cdot Y_n\\}$ is given in terms of the rate function of $\\{(X_n,Y_n)\\}$. A similar result for stochastic differential equations also holds. Since many Markov processes can be represented as solutions of stochastic differential equations, these results, in particular, provide a new approach to the study of large deviation principle for a sequence of Markov processes.",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-08-23T21:52:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G51",
      "60H05",
      "60H10",
      "60J25",
      "60J60"
    ],
    "keywords": [
      "stochastic differential equations driven",
      "stochastic integrals",
      "infinite-dimensional semimartingales",
      "large deviation principle holds",
      "markov processes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}