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math.PR2026
Special Dirichlet Processes: Structure, Uniqueness and Stability
Philip Kennerberg
We introduce the class of \emph{Special--Dirichlet processes}, consisting of càdlàg adapted processes admitting a decomposition \[ X=M+Γ, \] where \(M\) is a local martingale and \…
math.PR2026
Stability of compensator integrals and nonlinear operators under canonical p-th power variation convergence
Philip Kennerberg
Let \(X\) and \((X^n)_{n\ge1}\) be c`adl`ag processes with predictable compensators \(ν\) and \(ν^n\). For \(p>1\), assume that \([X^n-X]^{(p)}_t\to0\) in probability, where \([\,\…
math.FA2026
An Extremal Reconstruction Principle under Covariance Domination
Philip Kennerberg
We identify a structural extremal principle governing residual \(L^2\)-norms over operator-ordered covariance envelopes. In contrast to the centered setting, where such quantities…