Summary
Let (N t) and (Y t), t in [0,1], be stochastic processes on (Ω, ℬ, P). Suppose that (N t) is Gaussian, m.s. continuous, zero mean, and vanishes a.s. at t=0. Let v Y and v N be the induced measures on ℝ[0,1]. Conditions are obtained for v Y to be absolutely continuous w.r.t. v N. Expressions for the Radon-Nikodym derivative are derived. Further results on these problems are obtained for measures induced on L 2[0, 1] and on C[0, 1].
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Research supported by ONR Contracts N 00014-75-C-0491 and N 00014-81-K-0373
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Baker, C.R., Gualtierotti, A.F. Discrimination with respect to a Gaussian process. Probab. Th. Rel. Fields 71, 159–182 (1986). https://doi.org/10.1007/BF00332309
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DOI: https://doi.org/10.1007/BF00332309
Keywords
- Stochastic Process
- Probability Theory
- Statistical Theory
- Gaussian Process