EXPLICIT FILTERS FOR DIFFUSIONS WITH CERTAIN NONLINEAR DRIFTS.

D. L. OCONE, J. S. BARAS, S. I. MARCUS

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

LET X(T) BE A DIFFUSION SATISFYING THE STOCHASTIC DIFFERENTIAL EQUATION DX(T) = F(X(T))DT + DB(T), WHERE F ' (X) = F**2(X) = AX**2 + BX + C, A > 0. V. BENES GAVE AN EXPLICIT FORMULA FOR THE CONDITIONAL DENSITY OF X(T) GIVEN Y(S), 0 < S < T, WHERE Y(S) = ″INTEGRAL″ **T//0X(S)DS + W(T), WHEN W( * ) IS A BROWNIAN PROCESS INDEPENDENT OF X( * ). THE RESULT IS EXTENDED AND THEN APPLIED TO DERIVE RECURSIVE FILTERING EQUATIONS FOR ESTIMATING CONDITIONAL MOMENTS, FOR ESTIMATING POLYNOMIAL FUNCTIONALS OF X( * ), AND FOR SMOOTHING.

Original languageEnglish (US)
Pages (from-to)1-16
Number of pages16
JournalSTOCHASTICS
VolumeV 8
Issue numberN 1
DOIs
StatePublished - 1982

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modeling and Simulation

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