The paper solves the problem of minimization of the Kullback divergence between a partially known and a completely known probability distribution. It considers two probability distributions of a random vector (u1,x1,...,uT,xT) on a sample space of 2T dimensions. One of the distributions is known, the other is known only partially. Namely, only the conditional probability distributions of xτ given u1,x1,...,uτ−1,xτ−1,uτ are known for τ=1,...,T. Our objective is to determine the remaining conditional probability distributions of uτ given u1,x1,...,uτ−1,xτ−1 such that the Kullback divergence of the partially known distribution with respect to the completely known distribution is minimal. Explicit solution of this problem has been found previously for Markovian systems in Karný \cite{Karny:96a}. The general solution is given in this paper.
Let $H$ be a Hilbert space and $E$ a Banach space. We set up a theory of stochastic integration of ${\cal L}(H,E)$-valued functions with respect to $H$-cylindrical Liouville fractional Brownian motion with arbitrary Hurst parameter $0<\beta <1$. For $0<\beta <\frac 12$ we show that a function $\Phi \colon (0,T)\to {\cal L}(H,E)$ is stochastically integrable with respect to an $H$-cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an $H$-cylindrical fractional Brownian motion. We apply our results to stochastic evolution equations $$ {\rm d}U(t) = AU(t) {\rm d}t + B {\rm d}W_H^\beta (t) $$ driven by an $H$-cylindrical Liouville fractional Brownian motion, and prove existence, uniqueness and space-time regularity of mild solutions under various assumptions on the Banach space $E$, the operators $A\colon \scr D(A)\to E$ and $B\colon H\to E$, and the Hurst parameter $\beta $. As an application it is shown that second-order parabolic SPDEs on bounded domains in $\mathbb R^d$, driven by space-time noise which is white in space and Liouville fractional in time, admit a mild solution if $\frac {1}{4}d<\beta <1$.
In this paper we present the existence and uniqueness of solutions to the stochastic fuzzy differential equations driven by Brownian motion. The continuous dependence on initial condition and stability properties are also established. As an example of application we use some stochastic fuzzy differential equation in a model of population dynamics.
In applications of geometric programming, some coefficients and/or exponents may not be precisely known. Stochastic geometric programming can be used to deal with such situations. In this paper, we shall indicate which stochastic programming approaches and which structural and distributional assumptions do not destroy the favorable structure of geometric programs. The already recognized possibilities are extended for a tracking model and stochastic sensitivity analysis is presented in the context of metal cutting optimization. Illustrative numerical results are reported.
Optimization problems with stochastic dominance constraints are helpful to many real-life applications. We can recall e. g., problems of portfolio selection or problems connected with energy production. The above mentioned constraints are very suitable because they guarantee a solution fulfilling partial order between utility functions in a given subsystem U of the utility functions. Especially, considering U:=U1 (where U1 is a system of non decreasing concave nonnegative utility functions) we obtain second order stochastic dominance constraints. Unfortunately it is also well known that these problems are rather complicated from the theoretical and the numerical point of view. Moreover, these problems goes to semi-infinite optimization problems for which Slater's condition is not necessary fulfilled. Consequently it is suitable to modify the constraints. A question arises how to do it. The aim of the paper is to suggest one of the possibilities how to modify the original problem with an "estimation" of a gap between the original and a modified problem. To this end the stability results obtained on the base of the Wasserstein metric corresponding to L1 norm are employed. Moreover, we mention a scenario generation and an investigation of empirical estimates. At the end attention will be paid to heavy tailed distributions.
In classic data envelopment analysis models, two-stage network structures are studied in cases in which the input/output data set are deterministic. In many real applications, however, we face uncertainty. This paper proposes a two-stage network DEA model when the input/output data are stochastic. A stochastic two-stage network DEA model is formulated based on the chance-constrained programming. Linearization techniques and the assumption of single underlying factor of the data are used to construct the equivalent deterministic linear programming model. The relationship between the stochastic efficiency of each stage and stochastic centralized efficiency of the whole process, at different confidence levels, is discussed. To illustrate the real applicability of the proposed approach, a real case on 16 commercial banks in China is given.
The purpose of the paper is to introduce various stochastic programs and related deterministic reformulations that are suitable for engineering design problems,. Firstly, several application areas of engineering design are introduced and cited. Then, motivation ideas and basic concepts are presented. Later, various types of reformulations are introduced for decision problems involving uncertainty. In addition, short notes on comparison of optimal solutions are included. and Obsahuje seznam literatury
In 2017, 100 years elapsed since the introduction of the cosmological constant into the equations of general theory of relativity. In this paper we show which role the cosmological constant played in the beginning, what its status is today, and when it became a commonly accepted part of the physical description of reality as a suitable representative of the vacuum energy or, more generally, the so-called dark energy responsible for the current accelerated expansion of our universe. Finally, we discuss possible astrophysical manifestations of the cosmological constant., V roce 2017 uplynulo 100 let od zavedení kosmologické konstanty do rovnic obecné teorie relativity. V referátu ukazujeme, jakou roli hrála kosmologická konstanta na počátku a jaký je její status dnes, kdy se stala běžně přijímanou součástí fyzikálního popisu reality jako vhodný představitel energie vakua či obecně tzv. temné energie zodpovědné za současnou urychlovanou expanzi našeho vesmíru. Na závěr diskutujeme možné astrofyzikální projevy kosmologické konstanty., Petr Slaný, Zdeněk Stuchlík., and Obsahuje bibliografii
Stroke is despite of progressive improvements in treatment and
reperfusion strategies one of the most devastating human
pathology. However, as quality of acute health care improves and
more people survive ischemic attack, healthcare specialists have
to solve new challenges to preserve reasonable quality of life to
these patients. Thus, novel approaches which prevents
comorbidities of stroke and improve quality of life of stroke
survivors in general has to be developed and experimentally
tested. The aim of the present paper was to establish reliable rat
model of middle cerebral occlusion and set of methods allowing
selection of animals suitable for long-term experiments. We have
compared mortality rates, cerebral blood flow and extension of
ischemic lesion induced by intraluminal filament in three widely
used outbred rat strains. We have additionally used an animal
18F-DG PET scans to verify its reliability in noninvasive detection
of ischemic infarct in acute period (24 h after MCAO) for selecting
animals eligible for long survival experiments. Our data clearly
indicates that high variability between rat strains might
negatively influence stroke induction by intraluminal thread
occlusion of middle cerebral artery. Most reliable outbred rat
strain in our hands was Sprague-Dawley where maximal
reduction of cerebral blood flow and extensive ischemic lesion
was observed. Contrary, Wistar rats exhibited higher mortality
and Long-Evans rats significantly smaller or no ischemic region in
comparison to Sprague-Dawley. Additionally, we have confirmed
a positron emission tomography with 18F-fluorodeoxyglucose as
suitable method to assess extension of ischemic region in acute
period after the experimental arterial occlusion in rats.