
Stochastic Optimal Control of Epidemic Processes in Networks
We approach the development of models and control strategies of suscepti...
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Mixing it up: A general framework for Markovian statistics beyond reversibility and the minimax paradigm
Up to now, the nonparametric analysis of multidimensional continuoustim...
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Nonparametric learning for impulse control problems
One of the fundamental assumptions in stochastic control of continuous t...
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Estimating the characteristics of stochastic damping Hamiltonian systems from continuous observations
We consider nonparametric invariant density and drift estimation for a c...
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Bootstrapping Neural Processes
Unlike in the traditional statistical modeling for which a user typicall...
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On the Impossibility of Statistically Improving Empirical Optimization: A SecondOrder Stochastic Dominance Perspective
When the underlying probability distribution in a stochastic optimizatio...
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Learning to reflect: A unifying approach for datadriven stochastic control strategies
Stochastic optimal control problems have a long tradition in applied probability, with the questions addressed being of high relevance in a multitude of fields. Even though theoretical solutions are well understood in many scenarios, their practicability suffers from the assumption of known dynamics of the underlying stochastic process, raising the statistical challenge of developing purely datadriven strategies. For the mathematically separated classes of continuous diffusion processes and Lévy processes, we show that developing efficient strategies for related singular stochastic control problems can essentially be reduced to finding rateoptimal estimators with respect to the supnorm risk of objects associated to the invariant distribution of ergodic processes which determine the theoretical solution of the control problem. From a statistical perspective, we exploit the exponential βmixing property as the common factor of both scenarios to drive the convergence analysis, indicating that relying on general stability properties of Markov processes is a sufficiently powerful and flexible approach to treat complex applications requiring statistical methods. We show moreover that in the Lévy case  even though per se jump processes are more difficult to handle both in statistics and control theory  a fully datadriven strategy with regret of significantly better order than in the diffusion case can be constructed.
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