1. Organization in finance prepared by stohastic differential equations with additive and nonlinear models and continuous optimizationPakize Taylan, Gerhard-Wilhelm Weber, 2008, izvirni znanstveni članek Opis: A central element in organization of financal means by a person, a company or societal group consists in the constitution, analysis and optimization of portfolios. This requests the time-depending modeling of processes. Likewise many processes in nature, technology and economy, financial processes suffer from stochastic fluctuations. Therefore, we consider stochastic differential equations (Kloeden, Platen and Schurz, 1994) since in reality, especially, in the financial sector, many processes are affected with noise. As a drawback, these equations are hard to represent by a computer and hard to resolve. In our paper, we express them in simplified manner of approximation by both a discretization and additive models based on splines. Our parameter estimation refers to the linearly involved spline coefficients as prepared in (Taylan and Weber, 2007) and the partially nonlinearly involved probabilistic parameters. We construct a penalized residual sum of square for this model and face occuring nonlinearities by Gauss-Newton's and Levenberg-Marquardt's method on determining the iteration step. We also investigate when the related minimization program can be written as a Tikhonov regularization problem (sometimes called ridge regression), and we treat it using continuous optimization techniques. In particular, we prepare access to the elegant framework of conic quadratic programming. These convex optimation problems are very well-structured, herewith resembling linear programs and, hence, permitting the use of interior point methods (Nesterov and Nemirovskii, 1993).
Ključne besede: stochastic differential equations, regression, statistical learning, parameter estimation, splines, Gauss-Newton method, Levenberg-Marquardt's method, smoothing, stability, penalty methods, Tikhonov regularization, continuous optimization, conic quadratic programming
Objavljeno v DKUM: 10.01.2018; Ogledov: 964; Prenosov: 116
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3. Some basic difference equations of Schrodinger boundary value problemsAndreas Ruffing, Maria Meiler, Andrea Bruder, 2009, izvirni znanstveni članek Opis: We consider special basic difference equations which are related to discretizations of Schrödinger equations on time scales with special symmetry properties, namely, so-called basic discrete grids. These grids are of an adaptive grid type. Solving the boundary value problem of suitable Schrödinger equations on these grids leads to completely new and unexpected analytic properties of the underlying function spaces. Some of them are presented in this work.
Ključne besede: differential equations, discretization, Schrödinger equations, value problems
Objavljeno v DKUM: 26.06.2017; Ogledov: 890; Prenosov: 362
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4. Henríquez, Hernán; Hernández M., Eduardo; dos Santos, José: Asymptotically almost periodic and almost periodic solutions for partial neutral integrodifferential equations. (English). - [J] Z. Anal. Anwend. 26, No. 3, 363-375 (2007). [ISSN 0232-2064; ISSN 1661-4534]Miklavž Mastinšek, 2008, recenzija, prikaz knjige, kritika Ključne besede: matematika, diferencialne enačbe, mathematics, differential equations, neutral equations
Objavljeno v DKUM: 10.07.2015; Ogledov: 821; Prenosov: 24
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5. Liu, Xin-Ge; Wu, Min; Martin, Ralph; Tang, Mei-Lan: Delay-dependent stability analysis for uncertain neutral systems with time-varying delays. (English). - [J] Math. Comput. Simul. 75, No. 1-2, 15-27 (2007). [ISSN 0378-4754]Miklavž Mastinšek, 2008, recenzija, prikaz knjige, kritika Ključne besede: matematika, navadne diferencialne enačbe, asimptotična stabilnost, mathematics, ordinary differential equations, neutral delay-differential system
Objavljeno v DKUM: 10.07.2015; Ogledov: 1005; Prenosov: 34
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6. Bertoldi, Marcello; Fornaro, Simona; Lorenzi, Luca: Pointwise gradient estimates in exterior domains. (English). - [J] Arch. Math. 88, No. 1, 77-89 (2007). [ISSN 0003-889X; ISSN 1420-8938]Miklavž Mastinšek, 2007, recenzija, prikaz knjige, kritika Ključne besede: matematika, parcialne diferencialne enačbe, teorija operatorjev, neomejeni koeficienti, problem Cauchy-Neumanna, polgrupe Markova, mathematics, partial differential equations, operator theory, functional differential equation, unbounded coefficients, Cauchy-Neumann problem, Markov semigroup
Objavljeno v DKUM: 10.07.2015; Ogledov: 1025; Prenosov: 37
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7. Faria, Teresa: Asymptotic stability for delayed logistic type equations. (English). - [J] Math. Comput. Modelling 43, No. 3-4, 433-445 (2006). [ISSN 0895-7177]Miklavž Mastinšek, 2008, recenzija, prikaz knjige, kritika Ključne besede: matematika, navadne diferencialne enačbe, populacijska dinamika, mathematics, differential equations, delayed logistic equation, delayed population model, global asymptotic stability
Objavljeno v DKUM: 10.07.2015; Ogledov: 1185; Prenosov: 19
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8. Balachandran, K.; Ravikumar, R.: Nonlocal Cauchy problem for time varying delay integrodifferential equations of Sobolev type in Banach spaces. (English). - [J] Tamkang J. Math. 37, No. 3, 193-205 (2006). [ISSN 0049-2930]Miklavž Mastinšek, 2008, recenzija, prikaz knjige, kritika Ključne besede: matematika, navadne diferencialne enačbe, polgrupe nelinearnih operatorjev, mathematics, differential equations, delay integrodifferential equation, nonlocal condition
Objavljeno v DKUM: 10.07.2015; Ogledov: 719; Prenosov: 40
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9. Fu, Xianlong; Liu, Xingbo: Existence of solutions for neutral non-autonomous evolution equations with nonlocal conditions. (English). - [J] Indian J. Pure Appl. Math. 37, No. 3, 179-192 (2006). [ISSN 0019-5588]Miklavž Mastinšek, 2008, recenzija, prikaz knjige, kritika Ključne besede: matematika, diferencialne enačbe, funkcijske enačbe, mathematics, differential equations, neutral functional
Objavljeno v DKUM: 10.07.2015; Ogledov: 845; Prenosov: 33
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10. Golaszewska, Agata: Generalized solution of mixed problems for first order partial differential equations with state dependent delays. (English). - [J] Int.J. Pure Appl. Math. 29, No. 3, 349-384 (2006). [ISSN 1311-8080]Miklavž Mastinšek, 2008, recenzija, prikaz knjige, kritika Ključne besede: matematika, parcialne diferencialne enačbe, Volterrov integralski operator, zvezna odvisnost, funkcijske enačbe za realne funkcije, eksistenca, mathematics, partial differential equations, successive approximations, Volterra integral operator, existence, continuous dependence
Objavljeno v DKUM: 10.07.2015; Ogledov: 960; Prenosov: 36
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