Special weak Dirichlet processes and BSDEs driven by a random measure

2015/12/19 by Elena Bandini, Bandini, Elena, Francesco Paolo Russo +1 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Bayesian Methods and Mixture Models #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.1512.06234

openalex publication_date 2015/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper considers a forward BSDE driven by a random measure, when the underlying forward process X is special semimartingale, or even more generally, a special weak Dirichlet process. Given a solution (Y, Z, U), generally Y appears to be of the type u(t, X_t) where u is a deterministic function. In this paper we identify Z and U in terms of u applying stochastic calculus with respect to weak Dirichlet processes.

Cited by

• C ^0,1 -Itô chain rules and generalized solutions of parabolic PDEs

Related

• Weak Dirichlet processes and generalized martingale problems
• Natural decomposition of processes and weak Dirichlet processes
• Characteristics and Itô's formula for weak Dirichlet processes: an equivalence result
• Infinite dimensional weak Dirichlet processes and convolution type processes
• Infinite dimensional weak Dirichlet processes, stochastic PDEs and optimal control