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pro vyhledávání: '"Redmann, Martin"'
Autor:
Redmann, Martin
In this paper, we establish new strategies to reduce the dimension of large-scale controlled stochastic differential equations with non-zero initial states. The first approach transforms the original setting into a stochastic system with zero initial
Externí odkaz:
http://arxiv.org/abs/2408.00581
Autor:
Jamshidi, Nahid, Redmann, Martin
In this paper, we investigate large-scale linear systems driven by a fractional Brownian motion (fBm) with Hurst parameter $H\in [1/2, 1)$. We interpret these equations either in the sense of Young ($H>1/2$) or Stratonovich ($H=1/2$). Especially frac
Externí odkaz:
http://arxiv.org/abs/2307.04614
Autor:
Redmann, Martin, Riedel, Sebastian
In this paper, practically computable low-order approximations of potentially high-dimensional differential equations driven by geometric rough paths are proposed and investigated. In particular, equations are studied that cover the linear setting, b
Externí odkaz:
http://arxiv.org/abs/2306.17579
Autor:
Damm, Tobias, Redmann, Martin
In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic systems are id
Externí odkaz:
http://arxiv.org/abs/2303.13460
Autor:
Redmann, Martin
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such nonlinearities in hi
Externí odkaz:
http://arxiv.org/abs/2301.13722
Autor:
Redmann, Martin
Solving optimal stopping problems by backward induction in high dimensions is often very complex since the computation of conditional expectations is required. Typically, such computations are based on regression, a method that suffers from the curse
Externí odkaz:
http://arxiv.org/abs/2205.08951
Autor:
Redmann, Martin
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 July 2024 535(1)
Autor:
Redmann, Martin, Jamshidi, Nahid
This paper considers large-scale linear stochastic systems representing, e.g., spatially discretized stochastic partial differential equations. Since asymptotic stability can often not be ensured in such a stochastic setting (e.g. due to larger noise
Externí odkaz:
http://arxiv.org/abs/2109.10207
Autor:
Redmann, Martin, Duff, Igor Pontes
In this paper, we consider model order reduction for bilinear systems with non-zero initial conditions. We discuss choices of Gramians for both the homogeneous and the inhomogeneous parts of the system individually and prove how these Gramians charac
Externí odkaz:
http://arxiv.org/abs/2107.04269
Autor:
Redmann, Martin, Duff, Igor Pontes
In this paper, the problem of full state approximation by model reduction is studied for stochastic and bilinear systems. Our proposed approach relies on identifying the dominant subspaces based on the reachability Gramian of a system. Once the desir
Externí odkaz:
http://arxiv.org/abs/2102.07534