Multidimensional SDE with anticipating initial process and reflection

2007/04/20 by Zongxia Liang, Liang, Zongxia
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #(Primary) 60H07 #(Secondary) 60J55 #60H10 #60J50 #60J60 #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Risk and Portfolio Optimization #Stochastic processes and financial applications #math.PR #msc:60H07 #msc:60H10 #msc:60J50 #msc:60J55 #msc:60J60

paper · pdf · doi:10.48550/arxiv.0704.2715

25pages

arxiv created 2007/04/20 · openalex publication_date 2007/04/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, the strong solutions (X, L) of multidimensional stochastic differential equations with reflecting boundary and possible anticipating initial random variables is established. The key is to obtain some substitution formula for Stratonovich integrals via a uniform convergence of the corresponding Riemann sums and to prove continuity of functionals of (X, L).

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