arXiv subjects

Kristian P. Evans

Publications and source records attributed to Kristian P. Evans.

2 recordsLinked to original sources

arXiv2019

On Adjoint Additive Processes

Starting with an additive process $(Y_t)_{t\geq0}$, it is in certain cases possible to construct an adjoint process $(X_t)_{t\geq0}$ which is itself additive. Moreover, assuming that the transition densities of $(Y_t)_{t\geq0}$ are controlled by a natural pair of metrics $\mathrm{d}_{ψ,t}$ and $δ_{ψ,t}$, we can prove that the transition densities of $(X_t)_{t\geq0}$ are controlled by the metrics $δ_{ψ,1/t}$ replacing $\mathrm{d}_{ψ,t}$ and $\mathrm{d}_{ψ,1/t}$ replacing $δ_{ψ,t}$.

math.FA↗

arXiv2006

Feller Semigroups Obtained by Variable Order Subordination

For certain classes of negative definite symbols $q(x,ξ)$ and state space dependent Bernstein function $f(x,s)$ we prove that $-p(x,D)$, the pseudo-differential operator with symbol $-p(x,ξ)=-f(x,q(x,ξ))$, extends to the generator of a Feller semigroup. Our result extends previously known results related to operators of variable (fractional) order of differentiation, or variable order fractional powers. New concrete examples are given.

math.FA↗