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27422. On exact null controllability of Black-Scholes equation
- Creator:
- Sakthivel, Kumarasamy, Balachandran, Krishnan, Sowrirajan, Rangarajan, and Kim, Jeong-Hoon
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Black-Scholes equation, volatility, controllability, observability, and Carleman estimates
- Language:
- English
- Description:
- In this paper we discuss the exact null controllability of linear as well as nonlinear Black-Scholes equation when both the stock volatility and risk-free interest rate influence the stock price but they are not known with certainty while the control is distributed over a subdomain. The proof of the linear problem relies on a Carleman estimate and observability inequality for its own dual problem and that of the nonlinear one relies on the infinite dimensional Kakutani fixed point theorem with L2 topology.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
27423. On exact solutions of a class of interval boundary value problems
- Creator:
- Gasilov, Nizami A.
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- interval differential equations, boundary value problem, bunch of functions, and linear differential equations
- Language:
- English
- Description:
- In this article, we deal with the Boundary Value Problem (BVP) for linear ordinary differential equations, the coefficients and the boundary values of which are constant intervals. To solve this kind of interval BVP, we implement an approach that differs from commonly used ones. With this approach, the interval BVP is interpreted as a family of classical (real) BVPs. The set (bunch) of solutions of all these real BVPs we define to be the solution of the interval BVP. Therefore, the novelty of the proposed approach is that the solution is treated as a set of real functions, not as an interval-valued function, as usual. It is well-known that the existence and uniqueness of the solution is a critical issue, especially in studying BVPs. We provide an existence and uniqueness result for interval BVPs under consideration. We also present a numerical method to compute the lower and upper bounds of the solution bunch. Moreover, we express the solution by an analytical formula under certain conditions. We provide numerical examples to illustrate the effectiveness of the introduced approach and the proposed method. We also demonstrate that the approach is applicable to non-linear interval BVPs.
- Rights:
- http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public
27424. On experimental system for multidimensional model development MUDIM
- Creator:
- Jiroušek, Radim
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- probability, multidimensional distribution, composition, program package, and language R
- Language:
- English
- Description:
- Several systems supporting development and application of graphical Markov inodels are widely used; perliaps the most famous are HUGIN and NETICA, which are supporting Bayesian networks. The goal of this paper is to introduce system MUDIM, which is intended to support non-graphical multidimensional models, namely cornpositional models. The basic idea of these inodels resembles jig-saw puzzle, where a picture must be assembled from a great number of pieces, each bearing a small part of a picture. Analogously, compositional models of a multidimensional distribution are assenililed (composed) of a great number of low-dirnensional distributions. One of the advantages of this approach is that the same apparatus that is based on operators of composition, can be applied for description of both probabilistic and possibilistic models. This is also the goal for future MUDIM development, to extend it in the way that it will be able to process both probabilistic and possibilistic models.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
27425. On exponential stability of second order delay differential equations
- Creator:
- Agarwal, Ravi P, Domoshnitsky, Alexander, and Maghakyan, Abraham
- Format:
- print, bez média, and svazek
- Type:
- model:article and TEXT
- Subject:
- matematika, mathematics, delay equations, uniform exponential stability, exponential estimates of solutions, Cauchy function, 13, and 51
- Language:
- English
- Description:
- We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones. This method works not only for autonomous equations but also for equations with variable coefficients and delays., Ravi P. Agarwal, Alexander Domoshnitsky, Abraham Maghakyan., and Obsahuje seznam literatury
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
27426. On extensions of orthosymmetric lattice bimorphisms
- Creator:
- Toumi, Mohamed Ali
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- d-algebra, f-algebra, lattice homomorphism, and lattice bimorphism
- Language:
- English
- Description:
- In the paper we prove that every orthosymmetric lattice bilinear map on the cartesian product of a vector lattice with itself can be extended to an orthosymmetric lattice bilinear map on the cartesian product of the Dedekind completion with itself. The main tool used in our proof is the technique associated with extension to a vector subspace generated by adjoining one element. As an application, we prove that if (A, ∗) is a commutative d-algebra and A δ its Dedekind completion, then, A δ can be equipped with a d-algebra multiplication that extends the multiplication of A. Moreover, we indicate an error made in the main result of the paper: M. A. Toumi, Extensions of orthosymmetric lattice bimorphisms, Proc. Amer. Math. Soc. 134 (2006), 1615–1621.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
27427. On extensions of primary almost totally projective abelian groups
- Creator:
- Danchev, Peter Vassilev
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- totally projective group, almost totally projective group, countable group, and extension
- Language:
- English
- Description:
- Suppose G is a subgroup of the reduced abelian p-group A. The following two dual results are proved: (∗) If A/G is countable and G is an almost totally projective group, then A is an almost totally projective group. (∗∗) If G is countable and nice in A such that A/G is an almost totally projective group, then A is an almost totally projective group. These results somewhat strengthen theorems due to Wallace (J. Algebra, 1971) and Hill (Comment. Math. Univ. Carol., 1995), respectively.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
27428. On extremal dependence of block vectors
- Creator:
- Ferreira, Helena and Ferreira, Marta
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- multivariate extreme value theory, tail dependence, and extremal coefficients
- Language:
- English
- Description:
- Due to globalization and relaxed market regulation, we have assisted to an increasing of extremal dependence in international markets. As a consequence, several measures of tail dependence have been stated in literature in recent years, based on multivariate extreme-value theory. In this paper we present a tail dependence function and an extremal coefficient of dependence between two random vectors that extend existing ones. We shall see that in weakening the usual required dependence allows to assess the amount of dependence in d-variate random vectors based on bidimensional techniques. Simple estimators will be stated and can be applied to the well-known \emph{stable tail dependence function}. Asymptotic normality and strong consistency will be derived too. An application to financial markets will be presented at the end.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
27429. On extremal sizes of locally $k$-tree graphs
- Creator:
- Borowiecki, Mieczysław , Borowiecki, Piotr, Sidorowicz, Elżbieta , and Skupień, Zdzisław
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- xtremal problems, local property, locally tree, and $k$-tree
- Language:
- English
- Description:
- A graph $G$ is a {\it locally $k$-tree graph} if for any vertex $v$ the subgraph induced by the neighbours of $v$ is a $k$-tree, $k\ge 0$, where $0$-tree is an edgeless graph, $1$-tree is a tree. We characterize the minimum-size locally $k$-trees with $n$ vertices. The minimum-size connected locally $k$-trees are simply $(k+1)$-trees. For $k\ge 1$, we construct locally $k$-trees which are maximal with respect to the spanning subgraph relation. Consequently, the number of edges in an $n$-vertex locally $k$-tree graph is between $\Omega (n)$ and $O(n^2)$, where both bounds are asymptotically tight. In contrast, the number of edges in an $n$-vertex $k$-tree is always linear in $n$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
27430. On finite time stability with guaranteed cost control of uncertain linear systems
- Creator:
- Qayyum, Atif and Pironti, Alfredo
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- differential LMIs, finite time stability, guaranteed cost control, robust control, and state feedback control
- Language:
- English
- Description:
- This paper deals with the design of a robust state feedback control law for a class of uncertain linear time varying systems. Uncertainties are assumed to be time varying, in one-block norm bounded form. The proposed state feedback control law guarantees finite time stability and satisfies a given bound for an integral quadratic cost function. The contribution of this paper is to provide a sufficient condition in terms of differential linear matrix inequalities for the existence and the construction of the proposed robust control law. In particular, the construction of the feedback control law is brought back to a feasibility problem which can be solved inside the convex optimization framework. The effectiveness of the proposed approach is shown by means of the results obtained on a numerical and a physical example.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public