DSpace Collection: Volume 35, Number 4
http://hdl.handle.net/10525/2631
Serdica Mathematical Journal Volume 35, Number 4, 2009The Collection's search engineSearch the Channelsearch
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Fractional Korovkin Theory Based on Statistical Convergence
http://hdl.handle.net/10525/2677
Title: Fractional Korovkin Theory Based on Statistical Convergence<br/><br/>Authors: Anastassiou, George A.; Duman, Oktay<br/><br/>Abstract: In this paper, we obtain some statistical Korovkin-type approximation theorems including fractional derivatives of functions. We also show that our new results are more applicable than the classical ones.<br/><br/>Description: 2000 Mathematics Subject Classification: 41A25, 41A36, 40G15.Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast
http://hdl.handle.net/10525/2676
Title: Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast<br/><br/>Authors: Dia, Galaye; Kone, Abdoulaye<br/><br/>Abstract: We estimate a regression function on a point process by the Tukey regressogram method in a general setting and we give an application in the case of a Risk Process. We show among other things that, in classical Poisson model with parameter r, if W is the amount of the claim with finite espectation E(W) = m, Sn (resp. Rn) the accumulated interval waiting time for successive claims (resp. the aggregate claims amount) up to the nth arrival, the regression curve of R on S predicts ruin arrival time when the premium intensity c is less than rm whatever be the initial reverve.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators
http://hdl.handle.net/10525/2675
Title: Potapov-Ginsburg Transformation and Functional Models of Non-Dissipative Operators<br/><br/>Authors: Zolotarev, Vladimir A.; Hatamleh, Raéd<br/><br/>Abstract: A relation between an arbitrary bounded operator A and dissipative operator A+, built by A in the following way A+ = A+ij*Q-j, where A-A* = ij*Jj, (J = Q+-Q- is involution), is studied. The characteristic functions of the operators A and A+ are expressed by each other using the known Potapov-Ginsburg linear-fractional transformations. The explicit form of the resolvent (A-lI)-1 is expressed by (A+-lI)-1 and (A+*-lI)-1 in terms of these transformations. Furthermore, the functional model [10, 12] of non-dissipative operator A in terms of a model for A+, which evolves the results, was obtained by Naboko, S. N. [7]. The main constructive elements of the present construction are shown to be the elements of the Potapov-Ginsburg transformation for corresponding characteristic functions. A relation between an arbitrary bounded operator A and dissipative operator A+, built by A in the following way A+ = A + iϕ<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 47A20, 47A45; Secondary 47A48.Probabilistic Approach to the Neumann Problem for a Symmetric Operator
http://hdl.handle.net/10525/2673
Title: Probabilistic Approach to the Neumann Problem for a Symmetric Operator<br/><br/>Authors: Benchérif-Madani, Abdelatif<br/><br/>Abstract: We give a probabilistic formula for the solution of a non-homogeneous Neumann problem for a symmetric nondegenerate operator of second order in a bounded domain. We begin with a g-Hölder matrix and a C^1,g domain, g > 0, and then consider extensions. The solutions are expressed as a double layer potential instead of a single layer potential; in particular a new boundary function is discovered and boundary random walk methods can be used for simulations. We use tools from harmonic analysis and probability theory.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.