2017/04/12 by Adrien Barrasso, Barrasso, Adrien, Francesco Russo +1
Economics, Econometrics and Finance · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1704.03650
openalex publication_date 2017/04/12 · openalex created_date 2018/06/21 · openalex updated_date 2026/07/28
Let (ℙs,x)(s,x)∈[0,T]× E be a family of probability measures, where E is a Polish space,defined on the canonical probability space \mathbb D([0,T],E) of E-valued cadlag functions. We suppose that a martingale problem with respect to a time-inhomogeneous generator a is well-posed. We consider also an associated semilinear \it Pseudo-PDE with generator a for which we introduce a notion of so called \it decoupled mild solution and study the equivalence with the notion of martingale solution introduced in a companion paper. We also investigate well-posedness for decoupled mild solutions and their relations with a special class of BSDEs without driving martingale. The notion of decoupled mild solution is a good candidate to replace the notion of viscosity solution which is not always suitable when the map a is not a PDE operator.