2006/04/10 by Frederik Herzberg, Frederik S Herzberg, Herzberg, Frederik S
Economics, Econometrics and Finance · Mathematics · #03H05 #28E05 #60J65 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 28C20 #Probability (math.PR) #Secondary 44A60 #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #advanced mathematical theories #math.FA #math.PR #msc:03H05 #msc:28C20 #msc:28E05 #msc:44A60 #msc:60J65
paper · pdf · doi:10.48550/arxiv.math/0604211
14 pages; Theorem 2 and Lemma 1 withdrawn
openalex publication_date 2006/04/10 · arxiv created 2006/12/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Consider an L1-continuous functional ℓ on the vector space of polynomials of Brownian motion at given times, suppose ℓ commutes with the quadratic variation in a natural sense, and consider a finite set of polynomials of Brownian motion at rational times, f1( b),...,fm( b), mapping the Wiener space to ℝ. In the spirit of Schmüdgen's solution to the finite-dimensional moment problem, we give sufficient conditions under which ℓ can be written in the form ∫ ⋅ dμ for some finite measure μ on the Wiener space such that μ-almost surely, all the random variables f1( b),...,fm( b) are nonnegative.