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<p>In this paper, we present the testing of many hypotheses on multiple streams of observations that are driven by Lévy processes. This is applicable for sequential decision-making on the state of multi-sensor systems. In one case, each sensor receives or does not receive a signal obstructed by noise. In another, each sensor receives data driven by Lévy processes with large or small jumps. In either case, these give rise to <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2^n\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>2</mn> <mi>n</mi> </msup> </math></EquationSource> </InlineEquation> possibilities. Infinitesimal generators are presented and analyzed. Bounds for infinitesimal generators in terms of <i>super-solutions</i> and <i>sub-solutions</i> are computed. An application of this procedure for the stochastic model is also presented in relation to the financial market.</p>

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Hypothesis Tests on High-Dimensional Data Streams with Application in Financial Market

  • 期刊论文

  • 发表日期：

    2026年4月1日

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  • Michael Roberts,
  • Jessica Cao,
  • Shantanu Awasthi,
  • Indranil SenGupta

摘要

In this paper, we present the testing of many hypotheses on multiple streams of observations that are driven by Lévy processes. This is applicable for sequential decision-making on the state of multi-sensor systems. In one case, each sensor receives or does not receive a signal obstructed by noise. In another, each sensor receives data driven by Lévy processes with large or small jumps. In either case, these give rise to \(2^n\) 2 n possibilities. Infinitesimal generators are presented and analyzed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. An application of this procedure for the stochastic model is also presented in relation to the financial market.