Mathematik und Statistikhttps://kops.uni-konstanz.de:443/handle/123456789/82020-08-08T01:33:18Z2020-08-08T01:33:18ZParameter-Dependent Stochastic Optimal Control in Finite Discrete TimeJamneshan, Asgarpop254373Kupper, Michaelpop243845Zapata-García, José Miguel123456789/504492020-08-05T12:25:41Z2020-07-17Parameter-Dependent Stochastic Optimal Control in Finite Discrete Time
Jamneshan, Asgar; Kupper, Michael; Zapata-García, José Miguel
We prove a general existence result in stochastic optimal control in discrete time, where controls, taking values in conditional metric spaces, depend on the current information and past decisions. The general form of the problem lies beyond the scope of standard techniques in stochastic control theory, the main novelty is a formalization in conditional metric space and the use of conditional analysis. We illustrate the existence result by several examples such as wealth-dependent utility maximization under risk constraints and utility maximization with a conditional dimension. We also provide a discussion as to how our methods compare to techniques based on random sets.
2020-07-17Jamneshan, AsgarKupper, MichaelZapata-García, José Miguel510We prove a general existence result in stochastic optimal control in discrete time, where controls, taking values in conditional metric spaces, depend on the current information and past decisions. The general form of the problem lies beyond the scope of standard techniques in stochastic control theory, the main novelty is a formalization in conditional metric space and the use of conditional analysis. We illustrate the existence result by several examples such as wealth-dependent utility maximization under risk constraints and utility maximization with a conditional dimension. We also provide a discussion as to how our methods compare to techniques based on random sets.SpringerJOURNAL_ARTICLEeng10.1007/s10957-020-01711-z0022-32391573-2878Journal of Optimization Theory and Applications2020-08-05T14:25:40+02:00123456789/39Journal of Optimization Theory and Applications ; 2020. - Springer. - ISSN 0022-3239. - eISSN 1573-2878true2020-08-05T12:25:40ZtrueThe Cauchy Problem for Thermoelastic Plates with Two TemperaturesRacke, Reinhardpop03677Ueda, Yoshihiropop507668123456789/45403.22020-07-30T13:04:53Z2020The Cauchy Problem for Thermoelastic Plates with Two Temperatures
Racke, Reinhard; Ueda, Yoshihiro
We consider the decay rates of solutions to thermoelastic systems in materials where, in contrast to classical thermoelastic models for Kirchhoff type plates, two temperatures are involved, related by an elliptic equation. The arising initial value problems deal with systems of partial differential equations involving Schr ödinger like equations, hyperbolic and elliptic equations. Depending on the model – with Fourier or with Cattaneo type heat conduction – we obtain polynomial decay rates without or with regularity loss. This way we obtain another example where the loss of regularity in the Cauchy problem corresponds to the loss of exponential stability in bounded domains. The well-posedness is done using semigroup theory in appropriate space reflecting the different regularity compared to the classical single temperature case, and the (optimal) decay estimates are obtained with sophisticated pointwise estimates in Fourier space.
2020Racke, ReinhardUeda, Yoshihiro510We consider the decay rates of solutions to thermoelastic systems in materials where, in contrast to classical thermoelastic models for Kirchhoff type plates, two temperatures are involved, related by an elliptic equation. The arising initial value problems deal with systems of partial differential equations involving Schr ödinger like equations, hyperbolic and elliptic equations. Depending on the model – with Fourier or with Cattaneo type heat conduction – we obtain polynomial decay rates without or with regularity loss. This way we obtain another example where the loss of regularity in the Cauchy problem corresponds to the loss of exponential stability in bounded domains. The well-posedness is done using semigroup theory in appropriate space reflecting the different regularity compared to the classical single temperature case, and the (optimal) decay estimates are obtained with sophisticated pointwise estimates in Fourier space.European Mathematical Society (EMS)JOURNAL_ARTICLEeng10.4171/ZAA/16530232-20641661-4534103129391Zeitschrift für Analysis und ihre Anwendungen2020-07-30T15:04:52+02:00123456789/39Zeitschrift für Analysis und ihre Anwendungen ; 39 (2020), 1. - S. 103-129. - European Mathematical Society (EMS). - ISSN 0232-2064. - eISSN 1661-4534true2020-07-30T13:04:52ZtrueEfficient Approximation of Flow Problems With Multiple Scales in TimeFrei, Stefanpop524711Richter, Thomas123456789/503872020-07-29T11:40:20Z2020-05-26Efficient Approximation of Flow Problems With Multiple Scales in Time
Frei, Stefan; Richter, Thomas
In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier--Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on a slow scale in time. We derive an averaging scheme that is of first order with respect to the ratio of time scales $\epsilon$. In order to cope with the problem of unknown initial data for the fast-scale problem, we assume near-periodicity in time. Moreover, we construct a second-order accurate time discretization scheme and derive a complete error analysis for a corresponding simplified ODE system. The resulting multiscale scheme does not ask for the continuous simulation of the fast-scale variable and shows powerful speedups up to 1:10,000 compared to a resolved simulation. Finally, we present some numerical examples for the full Navier--Stokes system to illustrate the convergence and performance of the approach.
2020-05-26Frei, StefanRichter, Thomas510In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier--Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on a slow scale in time. We derive an averaging scheme that is of first order with respect to the ratio of time scales $\epsilon$. In order to cope with the problem of unknown initial data for the fast-scale problem, we assume near-periodicity in time. Moreover, we construct a second-order accurate time discretization scheme and derive a complete error analysis for a corresponding simplified ODE system. The resulting multiscale scheme does not ask for the continuous simulation of the fast-scale variable and shows powerful speedups up to 1:10,000 compared to a resolved simulation. Finally, we present some numerical examples for the full Navier--Stokes system to illustrate the convergence and performance of the approach.Society for Industrial and Applied Mathematics (SIAM)JOURNAL_ARTICLEeng10.1137/19M12583961540-34591540-3467942969182Multiscale Modeling & Simulation2020-07-29T13:38:46+02:00123456789/39Multiscale Modeling & Simulation ; 18 (2020), 2. - S. 942-969. - Society for Industrial and Applied Mathematics (SIAM). - ISSN 1540-3459. - eISSN 1540-3467true2020-07-29T11:38:46ZQuasi-Ordered Rings : a uniform Study of Orderings and ValuationsMüller, Simonpop259969123456789/503802020-07-29T01:02:45Z2020Quasi-Ordered Rings : a uniform Study of Orderings and Valuations
Müller, Simon
2020Müller, Simon51006A05, 06F25, 06F99, 13A18DOCTORAL_THESISurn:nbn:de:bsz:352-2-22s99ripn6un3eng2020-07-28T11:31:51+02:00123456789/392020-07-28T09:31:51Z