FG Stochastik und ihre Anwendungen
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- Open Access (7)
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- Block-bootstrap (1)
- Itô–Krylov’s type formula (1)
- Non-parametric (1)
- Parametric (1)
- Resampling (1)
- Zvonkin transformation (1)
- bifurcation curve (1)
- discrete epidemic model (1)
- epidemic models (1)
- flip bifurcation (1)
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Research profile line
Since the initiation of two variants of the bootstrap method by Efron and Rubin in the late 1970s, a variety of advancements has emerged in the literature. The subsampling of blocks enabled the estimation of the actual variance of the sample mean. The equivalence of the data-level and the estimator-level resampling is easily established for the sample mean and estimators alike. For Rubin’s variant of the bootstrap we apply an algorithm by Diniz et al. which allows for the numerically stable computation of the sample-based cumulative distribution function of the estimator under investigation. No actual Monte-Carlo resampling is necessary in this setting and we demonstrate how we get access to the very small probabilities of the tails and moreover to confidence intervals. We do this at the example of a well-known test model that exhibits geometrically decaying spatial correlations. The analysis naturally applies to temporally correlated systems or to the correlations occurring in Markov chains, as well.
We further promote the idea of quantum inspiration and propose to equip cognitive systems not only with tensors for data representation but also for operation representation. We argue that these are two sides of the same coin. For experimental symbolic algorithms we introduce a suitable testbed and give its proper specification. We formalize our method of behavioural control with tensor algebra and discuss its implementation for our physical testbed realization.
We googled various numeral words from 28 languages. Different approaches
for the description of the data were investigated. In all of the 28 languages,
the found frequency-magnitude dependence fits better to a power law than
to an exponential law. The result can be used to distinguish grammatically correct
from incorrect numerals based on the prediction of search results.
This study investigates the dynamic behavior of an SIRS epidemic model in discrete time, focusing primarily on mathematical analysis. We identify two equilibrium points, disease-free and endemic, with our main focus on the stability of the endemic state. Using data from the US Department of Health and optimizing the SIRS model, we estimate model parameters and analyze two types of bifurcations: Flip and Transcritical. Bifurcation diagrams and curves are presented, employing the Carcasses method. for the Flip bifurcation and an implicit function approach for the Transcritical bifurcation. Finally, we apply constrained optimal control to the infection and recruitment rates in the discrete SIRS model. Pontryagin’s maximum principle is employed to determine the optimal controls. Utilizing COVID-19 data from the USA, we showcase the effectiveness of the proposed control strategy in mitigating the pandemic’s spread.
AbstractIn this paper we study existence and uniqueness of solution stochastic differential equations involving fractional integrals driven by Riemann-Liouville multifractional Brownian motion and a standard Brownian. Then, we obtain approximate numerical solution of our problem and colon cancer chemotherapy effect model are presented to confirm our results. We show that considering time dependent Hurst parameters play an important role to get more realistic results.
AbstractIn this paper we study a system of decoupled forward-backward stochastic differential equations driven by a G-Brownian motion (G-FBSDEs) with non-degenerate diffusion. Our objective is to establish the existence of a relaxed optimal control for a non-smooth stochastic optimal control problem. The latter is given in terms of a decoupled G-FBSDE. The cost functional is the solution of the backward stochastic differential equation at the initial time. The key idea to establish existence of a relaxed optimal control is to replace the original control problem by a suitably regularised problem with mollified coefficients, prove the existence of a relaxed control, and then pass to the limit.
