The logarithmic representation of infinitesimal generators is generalized to the cases when evolution operator unbounded. result applicable unbounded operators, where unboundedness an essential ingredient nonlinear analysis. In conclusion a general framework for identification between with operators established. A mathematical such indispensable rigorous treatment transforms: e.g., transforms a...

We derive comparison results for Markov processes with respect to stochastic orderings induced by function classes. Our main result states that stochastic monotonicity of one process and comparability of the infinitesimal generators implies ordering of the processes. Unlike in previous work no boundedness assumptions on the function classes are needed anymore. We also present an integral versio...

We consider Landau’s type inequalities of the form ‖Aku‖n ≤ Cn,k‖u‖n−k‖Anu‖k, u ∈ D(A), 0 < k < n, where A is the infinitesimal generator of either a strongly continuous semigroup or a strongly continuous cosine function of linear contractions on a Banach space X. The constants Cn,k are computed for n ≤ 6.

The Nyquist Stability Criterion is generalized to systems where the (open-loop) system has infinite-dimensional input/output spaces and a (possibly) unbounded infinitesimal generator. This is done through use of the perturbation determinant and an extension of the Argument Principle to infinitesimal generators with trace-class resolvent.

We provide algorithms to compute the performance derivatives of Markov chains with respect to changes in their transition matrices and of Markov processes with respect to changes in their infinitesimal generators. Our algorithms are readily applicable to the control and optimization of these Markov systems, since they are based on analyzing a single sample path and do not need explicit specific...