2016/08/20 by Zdzisław Brzeźniak, Brzezniak, Zdzislaw, Tayfun Kok +1
Economics, Econometrics and Finance · Engineering · Mathematics · #Advanced Harmonic Analysis Research #FOS: Economics and business #Mathematical Finance (q-fin.MF) #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1608.05814
openalex publication_date 2016/08/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the stochastic evolution equation (1.1) in martingale-type 2 Banach spaces (with the linear part of the drift being only a generator of a C0-semigroup). We prove the existence and the uniqueness of solutions to this equation. We apply the abstract results to the Heath-Jarrow-Morton-Musiela (HJMM) equation (6.3). In particular, we prove the existence and the uniqueness of solutions to the latter equation in the weighted Lebesgue and Sobolev spaces respectively. We also find a sufficient condition for the existence and the uniqueness of an invariant measure for the Markov semigroup associated to equation (6.3) in the weighted Lebesgue spaces.