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Wyświetlanie 1-15 z 19
Tytuł:
Stochastic model of drug concentration level during IV-administration
Autorzy:
Dzhalladova, Irada
Růžičková, Miroslava
Powiązania:
https://bibliotekanauki.pl/articles/29519179.pdf
Data publikacji:
2022
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
IV-administration
deterministic model
stochastic differential equation
mean value
delay differential equation
Opis:
A stochastic model describing the concentration of the drug in the body during its IV-administration is discussed. The paper compares a deterministic model created with certain simplifications with the stochastic model. Fluctuating and irregular patterns of plasma concentrations of some drugs observed during intravenous infusion are explained. An illustrative example is given with certain values of drug infusion rate and drug elimination rate.
Źródło:
Opuscula Mathematica; 2022, 42, 6; 833-847
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A general class of McKean-Vlasov stochastic evolution equations driven by Brownian motion and Lèvy process and controlled by Lèvy measure
Autorzy:
Ahmed, N.
Powiązania:
https://bibliotekanauki.pl/articles/729570.pdf
Data publikacji:
2016
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
McKean-Vlasov stochastic differential equation
Hilbert spaces
existence of optimal controls
Opis:
In this paper we consider McKean-Vlasov stochastic evolution equations on Hilbert spaces driven by Brownian motion and L`evy process and controlled by L`evy measures. We prove existence and uniqueness of solutions and regularity properties thereof. We consider weak topology on the space of bounded Le´vy measures on infinite dimensional Hilbert space and prove continuous dependence of solutions with respect to the Le´vy measure. Then considering a certain class of Le´vy measures on infinite as well as finite dimensional Hilbert spaces, as relaxed controls, we prove existence of optimal controls for Bolza problem and some simple mass transport problems
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2016, 36, 2; 181-206
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Backward stochastic variational inequalities driven by multidimensional fractional Brownian motion
Autorzy:
Borkowski, D.
Jańczak-Borkowska, K.
Powiązania:
https://bibliotekanauki.pl/articles/254731.pdf
Data publikacji:
2018
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
backward stochastic differential equation
fractional Brownian motion
backward stochastic variational inequalities
subdifferential operator
Opis:
We study the existence and uniqueness of the backward stochastic variational inequalities driven by m-dimensional fractional Brownian motion with Hurst parameters Hk (k = 1,... m) greater than 1/2. The stochastic integral used throughout the paper is the divergence type integral.
Źródło:
Opuscula Mathematica; 2018, 38, 3; 307-326
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimal control of general McKean-Vlasov stochastic evolution equations on Hilbert spaces and necessary conditions of optimality
Autorzy:
Ahmed, N.
Powiązania:
https://bibliotekanauki.pl/articles/729626.pdf
Data publikacji:
2015
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
McKean-Vlasov stochastic differential equation
Hilbert spaces
relaxed controls
existence of optimal controls
Opis:
In this paper we consider controlled McKean-Vlasov stochastic evolution equations on Hilbert spaces. We prove existence and uniqueness of solutions and regularity properties thereof. We use relaxed controls, adapted to a current of sub-sigma algebras generated by observable processes, and taking values from a Polish space. We introduce an appropriate topology based on weak star convergence. We prove continuous dependence of solutions on controls with respect to appropriate topologies. Theses results are then used to prove existence of optimal controls for Bolza problems. Then we develop the necessary conditions of optimality based on semi-martingale representation theory on Hilbert spaces. Next we show that the adjoint processes arising from the necessary conditions optimality can be constructed from the solution of certain BSDE.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2015, 35, 2; 165-195
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On potential kernels associated with random dynamical systems
Autorzy:
Hmissi, M.
Mokchaha, F.
Hmissi, A.
Powiązania:
https://bibliotekanauki.pl/articles/1397853.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
dynamical system
random dynamical systems
random differential equations
stochastic differential equation
potential kernel
domination principle
Lyapunov function
Opis:
Let $(\Theta;, \phi)$ be a continuous random dynamical system defined on a probability space $(\Omega, F, P)$ and taking values on a locally compact Hausdorff space E. The associated potential kernel V is given by $V f(\omega, x) = \int_0^\infty f (\Theta_t \omega, \phi(t, \omega)x)dt, \omega \in \Omega, x \in E$. In this paper, we prove the equivalence of the following statements: 1. The potential kernel of $(\Theta, \phi)$ is proper, i.e. $V f$ is x-continuous for each bounded, x-continuous function with uniformly random compact support. 2. $(\Theta, \phi)$ has a global Lyapunov function, i.e. a function $ L : \Omega \times E \rightarrow (0, \infty) $ which is x-continuous and $ L(\Theta_t\omega, \phi(t,\omega)x) \downarrow 0$ as $ t \uparrow \infty $. In particular, we provide a constructive method for global Lyapunov functions for gradient-like random dynamical systems. This result generalizes an analogous theorem known for deterministic dynamical systems.
Źródło:
Opuscula Mathematica; 2015, 35, 4; 499-515
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A Jurdjevic-Quinn theorem for stochastic differential systems under weak conditions
Autorzy:
Florchinger, Patrick
Powiązania:
https://bibliotekanauki.pl/articles/2183489.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
stochastic differential system
weak solution of stochastic differential equation
asymptotic stability in probability
Barbashin–Krasovskii theorem
stabilizing state feedback law
Opis:
The purpose of this paper is to provide sufficient conditions for the stabilizability of weak solutions of stochastic dif- ferential systems when both the drift and diffusion are affine in the control. This result extends the well–known theorem of Jurdjevic–Quinn (Jurdjevic and Quinn, 1978) to stochastic differential systems under weaker conditions on the system coefficients than those assumed in Florchinger (2002).
Źródło:
Control and Cybernetics; 2022, 51, 1; 21--29
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Equilibrium reinsurance-investment strategy for mean-variance insurers under state dependent risk aversion
Autorzy:
Alia, Ishak
Chighoub, Farid
Powiązania:
https://bibliotekanauki.pl/articles/1839127.pdf
Data publikacji:
2019
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
time inconsistency
mean-variance criterion
investment-reinsurance strategy
insurer
equilibrium strategy
forward-backward stochastic differential equation
Opis:
In this work, we study the equilibrium reinsurance/ new business and investment strategy for mean-variance insurers, under the assumption that the risk aversion is a function of current wealth level. The surplus of the agents is represented by a sum of a compound process and a linear premium perturbed with a Brownian component. The financial market consists of one riskless asset and a multiple risky assets whose price processes are driven by Poisson random measures and independent Brownian motions. We characterize explicit expressions for the time-consistent Nash equilibrium strategy and the equilibrium value function via a forward-backward stochastic system and an equilibrium condition. An interesting feature of these FBSDEs is that a time parameter is involved, so that they form a flow of FBSDEs. Furthermore, a feedback representation of an equilibrium solution is derived. This solution provides a tool for comparing the equilibrium strategy with those derived in other papers, where some special cases were studied by the dynamic programming argument.
Źródło:
Control and Cybernetics; 2019, 48, 4; 489-523
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Ruin probability in a risk model with variable premium intensity and risky investments
Autorzy:
Mishura, Y.
Perestyuk, M.
Ragulina, O.
Powiązania:
https://bibliotekanauki.pl/articles/254807.pdf
Data publikacji:
2015
Wydawca:
Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
Tematy:
risk process
infinite-horizon ruin probability
variable premium intensity
risky investments
exponential bound
stochastic differential equation
explosion time
existence and uniqueness theorem
supermartingale property
Opis:
We consider a generalization of the classical risk model when the premium intensity depends on the current surplus of an insurance company. All surplus is invested in the risky asset, the price of which follows a geometric Brownian motion. We get an exponential bound for the infinite-horizon ruin probability. To this end, we allow the surplus process to explode and investigate the question concerning the probability of explosion of the surplus process between claim arrivals.
Źródło:
Opuscula Mathematica; 2015, 35, 3; 333-352
1232-9274
2300-6919
Pojawia się w:
Opuscula Mathematica
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Nonlinear filtering for Markov systems with delayed observations
Autorzy:
Calzolari, A.
Florchinger, P.
Nappo, G.
Powiązania:
https://bibliotekanauki.pl/articles/907856.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
filtracja nieliniowa
proces dyfuzji
procesy Markova
stochastyczne równanie różniczkowe
nonlinear filtering
jump processes
diffusion processes
Markov processes
stochastic delay differential equation
Opis:
This paper deals with nonlinear filtering problems with delays, i.e., we consider a system (X,Y ), which can be represented by means of a system [...], in the sense that [...], where a(t) is a delayed time transformation. We start with X being a Markov process, and then study Markovian systems, not necessarily diffusive, with correlated noises. The interest is focused on the existence of explicit representations of the corresponding filters as functionals depending on the observed trajectory. Various assumptions on the function a(t) are considered.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2009, 19, 1; 49-57
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Robust Control of Linear Stochastic Systems with Fully Observable State
Autorzy:
Poznyak, Alexander
Taksar, M.
Powiązania:
https://bibliotekanauki.pl/articles/1339291.pdf
Data publikacji:
1996
Wydawca:
Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:
robust control
Riccati equation
stochastic differential equations
stochastic control
Opis:
We consider a multidimensional linear system with additive inputs (control) and Brownian noise. There is a cost associated with each control. The aim is to minimize the cost. However, we work with the model in which the parameters of the system may change in time and in addition the exact form of these parameters is not known, only intervals within which they vary are given. In the situation where minimization of a functional over the class of admissible controls makes no sense since the value of such a functional is different for different systems within the class, we should deal not with a single problem but with a family of problems. The objective in such a setting is twofold. First, we intend to establish existence of a state feedback linear robust control which stabilizes any system within the class. Then among all robust controls we find the one which yields the lowest bound on the cost within the class of all systems under consideration. We give the answer in terms of a solution to a matrix Riccati equation and we present necessary and sufficient conditions for such a solution to exist. We also state a criterion when the obtained bound on the cost is sharp, that is, the control we construct is actually a solution to the minimax problem.
Źródło:
Applicationes Mathematicae; 1996-1997, 24, 1; 35-46
1233-7234
Pojawia się w:
Applicationes Mathematicae
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A dynamic bi-orthogonal field equation approach to efficient Bayesian inversion
Autorzy:
Tagade, P. M.
Choi, H. L.
Powiązania:
https://bibliotekanauki.pl/articles/330516.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
Bayesian framework
stochastic partial differential equation
Karhunen–Loève expansion
generalized polynomial chaos
dynamically biorthogonal field equations
ramy Bayesa
stochastyczne równanie różniczkowe
przekształcenie Karhunena-Loeve'a
chaos wielomianowy
Opis:
This paper proposes a novel computationally efficient stochastic spectral projection based approach to Bayesian inversion of a computer simulator with high dimensional parametric and model structure uncertainty. The proposed method is based on the decomposition of the solution into its mean and a random field using a generic Karhunen–Loève expansion. The random field is represented as a convolution of separable Hilbert spaces in stochastic and spatial dimensions that are spectrally represented using respective orthogonal bases. In particular, the present paper investigates generalized polynomial chaos bases for the stochastic dimension and eigenfunction bases for the spatial dimension. Dynamic orthogonality is used to derive closed-form equations for the time evolution of mean, spatial and the stochastic fields. The resultant system of equations consists of a partial differential equation (PDE) that defines the dynamic evolution of the mean, a set of PDEs to define the time evolution of eigenfunction bases, while a set of ordinary differential equations (ODEs) define dynamics of the stochastic field. This system of dynamic evolution equations efficiently propagates the prior parametric uncertainty to the system response. The resulting bi-orthogonal expansion of the system response is used to reformulate the Bayesian inference for efficient exploration of the posterior distribution. The efficacy of the proposed method is investigated for calibration of a 2D transient diffusion simulator with an uncertain source location and diffusivity. The computational efficiency of the method is demonstrated against a Monte Carlo method and a generalized polynomial chaos approach.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2017, 27, 2; 229-243
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Stochastic differential inclusions of Langevin type on Riemannian manifolds
Autorzy:
Gliklikh, Yuri
Obukhovskiĭ, Andrei
Powiązania:
https://bibliotekanauki.pl/articles/729326.pdf
Data publikacji:
2001
Wydawca:
Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:
stochastic differential inclusions
Langevin equation
Riemannian manifolds
Opis:
We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.
Źródło:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization; 2001, 21, 2; 173-190
1509-9407
Pojawia się w:
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On the fuzzy control stochastic differential systems
Autorzy:
Tung, T. T.
Powiązania:
https://bibliotekanauki.pl/articles/970073.pdf
Data publikacji:
2013
Wydawca:
Polska Akademia Nauk. Instytut Badań Systemowych PAN
Tematy:
fuzzy theory
differential equations
fuzzy differential equation
fuzzy stochastic differential system
control theory
Opis:
In this paper, fuzzy control stochastic differentia systems are introduced. The existence and some comparison results on solutions of fuzzy control stochastic differential systems and on sheaf-solutions of sheaf fuzzy control stochastic systems are provided. The continuous dependence of solutions and sheaf-solutions on initials and controls is investigated. The results obtained are correct and meaningful for the theory control.
Źródło:
Control and Cybernetics; 2013, 42, 2; 505-525
0324-8569
Pojawia się w:
Control and Cybernetics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Approximation of the Zakai Equation in a Nonlinear Filtering Problem With Delay
Autorzy:
Twardowska, K.
Marnik, T.
Pasławska-Południak, M.
Powiązania:
https://bibliotekanauki.pl/articles/908197.pdf
Data publikacji:
2003
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
stochastic differential equations with delay
Zakai's equation
nonlinear filtering
matematyka
Opis:
A nonlinear filtering problem with delays in the state and observation equations is considered. The unnormalized conditional probability density of the filtered diffusion process satisfies the so-called Zakai equation and solves the nonlinear filtering problem. We examine the solution of the Zakai equation using an approximation result. Our theoretical deliberations are illustrated by a numerical example.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2003, 13, 2; 151-160
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Random vortex method for three dimensional flows. Part I: Mathematical background
Stochastyczna metoda wirowa dla przepływów trójwymiarowych. Część I: Podstawy matematyczne
Autorzy:
Styczek, A.
Duszyński, P.
Poćwierz, M.
Szumbarski, J.
Powiązania:
https://bibliotekanauki.pl/articles/281532.pdf
Data publikacji:
2004
Wydawca:
Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
Tematy:
vortex methods
vortex stretching
Fokker-Planck-Kolmogorow equation
Ito stochastic differential equations
Opis:
The paper presents a mathematical formulation of the Lagrangian method suitable for numerical simulation of 3D viscous incompressible flows. The vorticity field is approximated by a large ensemble of vortex particles which move with the fluid (advection) and perform random walks (diffusion). The charges of the particles change with time due to the stretching term in the governing equation. The construction of the vortex particles ensures that the approximated vorticity field is strictly divergence-free at any time instant. The boundary condition at the surface of an immersed body is satisfied by the creation of new vortex particles near the surface. Various properties of induced velocity and vorticity fields are also discussed.
W pracy sformułowano langranżowską metodę wirową dla trójwymiarowych przepływów cieczy lepkiej. Pole wirowści jest w niej aproksymowane zbiorem cząstek poruszających się wraz z płynem oraz wykonujących ruch losowy (dyfyzja). Ładunki wirowości niesione przez cząstki zależą od czasu (efekt "strechingu"). Konstrukcja cząstek zapewnia, że pole wirowości pozostaje bezźródłowe w trakcie symulacji. Warunek dla pola prędkości stawiany na powierzchni opływanego ciała jest realizowany drogą generacji nowych cząstek w sąsiedztwie tej powierzchni. W pracy przedyskutowano również własności indukowanego pola prędkości i wirowości.
Źródło:
Journal of Theoretical and Applied Mechanics; 2004, 42, 1; 3-20
1429-2955
Pojawia się w:
Journal of Theoretical and Applied Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 19

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