7 papers · 1 filter
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 \…
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 \([\,\…
Stability in quadratic variation
Philip Kennerberg, Magnus Wiktorsson
Consider a sequence of cadlag processes , and some fixed function . If is continuous then under several modes of convergence implies corresponding conv…
Stability in quadratic variation, with applications
Philip Kennerberg, Magnus Wiktorsson
We show that non continuous Dirichlet processes, defined as in \cite{NonCont} are closed under a wide family of locally Lipschitz continuous maps (similar to the time-homogeneous v…
A local barycentric version of the Bak-Sneppen model
Philip Kennerberg, Stanislav Volkov
We study the behaviour of the interacting particle system, arising from the Bak-Sneppen model and Jante's law process. Let vertices be placed on a circle, such that each vertex…
Convergence in the -contest
Philip Kennerberg, Stanislav Volkov
We study asymptotic properties of the following Markov system of points in~. At each time step, the point farthest from the current centre of mass, multiplied by…
Jante's law process
Philip Kennerberg, Stanislav Volkov
Consider the process which starts with distinct points on , and fix a positive integer~. Of the total points keep those which minimize the en…