We will recall the definition of semicontinuity of a function and some of related properties. (pdf) Continue reading
We recall definition of convergence in distribution and its related Portmanteau Theorem here. This is based on [Bil99] ([Patrick Billingsley 1999]).
Reference: [Bil99] ([Patrick Billingsley 1999])
Goal: RCLL space is the collection of all right continuous processes with left limit exists. In this below, we will give a definition of Skorohod metric on this space. More precisely, for a , we denote by the collection of RCLL processes on taking values in . We also use to denote the collection of RCLL processes on .
We have discussed the definition of viscosity property (here). In this note, we will discuss the definition of the viscosity solution of Dirichlet problem. (PDF) Continue reading
In this note, we will discuss the definition of the viscosity solution property. (PDF) Continue reading
Last Friday, I’ve had a pleasant discussion with Professor Lions (here) on my recent paper (here). PDF is also available (here).