Comparison results are given for time-inhomogeneous Markov processes with respect to function classes induced stochastic orderings. The main result states comparison of two processes, provided that the comparability of their infinitesimal generators as well as an invariance property of one process is assumed. The corresponding proof is based on a representation result for the solutions of inhomogeneous evolution problems in Banach spaces, which extends previously known results from the literature. Based on this representation, an ordering result for Markov processes induced by bounded and unbounded function classes is established. We give various applications to time-inhomogeneous diffusions, to processes with independent increments and to Lévy driven diffusion processes.

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Small and medium-sized enterprises (SME) face the challenge of making the best use of digital transformation, but they usually do not have the knowledge required to implement such transformations. Against this background, we suggest a process model that helps SME to identify the steps required to digitally transform their business model. We base the model on common approaches, which we adapted and extended for SME. Zusammenfassung Klein- und mittelständische Unternehmen (KMU) müssen ihre digitale Transformation gestalten, verfügen aber meist nicht über das notwendige Wissen darüber. Ein Vorgehensmodell wird vorgeschlagen, das die zur digitalen Transformation des Geschäftsmodells erforderlichen Phasen aufzeigt. Das Modell basiert auf allgemeinen Vorgehensweisen, die entsprechend für KMU angepasst und erweitert wurden.

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