Pflugfolgen

Pflugfolgen (Pflug sequences) is a term used in mathematics, particularly in stochastic optimization and risk management, to denote a class of sequences named after the mathematician Pflug. The exact definition is not universal; different authors use the term for various constructions that aim to approximate or study models under uncertainty. In general, a Pflugfolge may be a sequence of models, scenarios, distributions, or objective functionals that converge to a limiting problem or provide a coherent approximation to a risk measure.

Typical usage involves sequences of discretized scenarios S_n that approximate a stochastic program with a random vector Y; sequences of risk functionals R_n that converge to a target risk measure; or sequences of objective functions f_n that epi-converge to f. The analysis often focuses on convergence properties (in distribution, in probability, almost surely, or in Lp), stability under perturbations, and the preservation of optimal solutions or optimal values.

Applications include two-stage stochastic programming, CVaR and other coherent risk measures, and more broadly risk-averse optimization, where Pflugfolgen provide a framework to study how discretization and data-driven approximations affect solutions. They are used to justify numerical algorithms, scenario generation methods, and the passage from finite-sample problems to limiting problems.

See also: stochastic programming, risk measures, CVaR, epi-convergence, scenario generation. The term reflects a family of related ideas rather than a single fixed construction.