Philip Kennerberg

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 \(Γ\) is an adapted càdlàg process with vanishing continuous quadratic variation whose jumps are predictable and \(\mathcal …

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 \(Γ\) is an adapted càdlàg process with vanishing continuous quadratic variation whose jumps are predictable and \(\mathcal …

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Stability of Compensated Jump Integrals under Quadratic Variation Convergence

Philip Kennerberg

We study the stability of compensated jump integrals under convergence of quadratic variation alone. Let \(X\) and \(\{X^n\}_{n\ge1}\) be càdlàg processes with jump measures \(μ,μ_n\) and predictable compensators \(ν,ν_n\). Under the assumption \[ [X^n-X]_t \to 0 \qquad\text{in probability}, \] we establish ucp …

Stability of Compensated Jump Integrals under Quadratic Variation Convergence

Philip Kennerberg

We study the stability of compensated jump integrals under convergence of quadratic variation alone. Let \(X\) and \(\{X^n\}_{n\ge1}\) be càdlàg processes with jump measures \(μ,μ_n\) and predictable compensators \(ν,ν_n\). Under the assumption \[ [X^n-X]_t \to 0 \qquad\text{in probability}, \] we establish ucp …

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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 reduce to trace expressions involving covariance operators, the non-centered framework generates mixed terms that cannot be recovered from covariance ordering …

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 reduce to trace expressions involving covariance operators, the non-centered framework generates mixed terms that cannot be recovered from covariance ordering …

Stability in quadratic variation

Philip Kennerberg, Magnus Wiktorsson

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Constructive and consistent estimation of quadratic minimax

Philip Kennerberg, Ernst C. Wit

We consider $k$ square integrable random variables $Y_1,...,Y_k$ and $k$ random (row) vectors of length $p$, $X_1,...,X_k$ such that $X_i(l)$ is square integrable for $1\le i\le k$ and $1\le l\le p$. No assumptions whatsoever are made of any relationship between the $X_i$:s …

Stability in quadratic variation

Philip Kennerberg, Magnus Wiktorsson

Consider a sequence of cadlag processes $\{X^n\}_n$, and some fixed function $f$. If $f$ is continuous then under several modes of convergence $X^n\to X$ implies corresponding convergence of $f(X^n)\to f(X)$, due to continuous mapping. We study conditions (on $f$, $\{X^n\}_n$ and $X$) …

Optimal worst-risk minimization in structural equation models with random coefficients

Philip Kennerberg, Ernst C. Wit

The insight that causal parameters are particularly suitable for out-of-sample prediction has sparked a lot development of causal-like predictors. However, the connection with strict causal targets, has limited the development with good risk minimization properties, but without a direct causal interpretation. In …

Worst-risk minimization in generalized structural equation models

Philip Kennerberg, Ernst C. Wit

We consider rather general structural equation models (SEMs) between a target and its covariates in several shifted environments. Given $k\in\mathbb{N}$ shifts we consider the set of shifts that are at most $γ$-times as strong as a given weighted linear combination of these …

A Local Barycentric Version of the Bak–Sneppen Model

Philip Kennerberg, Stanislav Volkov

Abstract We study the behaviour of an interacting particle system, related to the Bak–Sneppen model and Jante’s law process defined in Kennerberg and Volkov (Adv Appl Probab 50:414–439, 2018). Let $$N\ge 3$$ N≥3 vertices be placed on a circle, such that each …

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