Construction of Exponential Martingales for Counting Processes.

Abstract

Let N(t) be a counting process with continuous compensator A(t) and f(t) a bounded predictabler process. If E(exp(2/f/N(t))) < infinity and E(exp (2(1 + exp/f/)A (t))) < infinity then it is shown that z(+) = exp (-integral from 0 to t (f(u)dN(u)) - integral from 0 to t (exp (-f(u)) - 1)dA(u) is a martingale. This is a partial extension of a theorem of Kabanov, Liptser, Shiryaev (1980) who assumed A(t) < or = but did not assume A(t) is continuous. Keywords: Random variables, Stochastic processes, Poisson processes, convergence.

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Document Details

Document Type
Technical Report
Publication Date
Apr 03, 1985
Accession Number
ADA160189

Entities

People

  • W. A. Rosenkrantz

Organizations

  • University of Massachusetts Amherst

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  • Materials and Manufacturing Processes

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Fields of Study

  • Mathematics

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  • Analytical Mechanics
  • Statistical inference.