2006/05/16 by Ali Süleyman Üstünel, Ustunel, Ali Suleyman, Moshe Zakai +1
Mathematics · #35J60 #46G12 #47H05 #47H1 #60G15 #60G30 #60G35 #60H05 #60H07 #60H25 #Algebraic and Geometric Analysis #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR) #Spectral Theory in Mathematical Physics #Statistics Theory (math.ST) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.math/0605433
openalex publication_date 2006/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let (W,H,μ) be the classical Wiener space. Assume that U=IW+u is an adapted perturbation of identity, i.e., u:W→ H is adapted to the canonical filtration of W. We give some sufficient analytic conditions on u which imply the invertibility of the map U. In particular it is shown that if u∈ \DDp,1(H) is adapted and if exp(1/2‖∇ u‖22-δu)∈ Lq(μ), where p-1+q-1=1, then IW+u is almost surely invertible. As a consequence, if, there exists an integer k≥ 1 such that ‖∇k u‖H⊗(k+1)∈ L^∞(μ), then IW+u is again almost surely invertible.