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Long-term and blow-up behaviors of exponential moments in multi-dimensional affine diffusions
Jena, R.P.,Kim, K.K.,Xing, H. North-Holland Pub. Co ; Elsevier Science Ltd 2012 Stochastic processes and their applications Vol.122 No.8
This paper considers multi-dimensional affine processes with continuous sample paths. By analyzing the Riccati system, which is associated with affine processes via the transform formula, we fully characterize the regions of exponents in which exponential moments of a given process do not explode at any time or explode at a given time. In these two cases, we also compute the long-term growth rate and the explosion rate for exponential moments. These results provide a handle to study implied volatility asymptotics in models where log-returns of stock prices are described by affine processes whose exponential moments do not have an explicit formula.
이상민(Sang-Min Lee),조중선(Joong-Seon Joh) 한국지능시스템학회 2001 한국지능시스템학회논문지 Vol.11 No.8
비선형 미분방정식으로부터 TSK(Takagi-Sugeno-Kang) 퍼지모델을 유도하는 것은 퍼지 제어의 이론분야에서는 매우 중요한 문제이다. 본 논문에서는 off-equilibrium에서 상수항을 가지는 부분 미분 방정식을 배제시키는 방법을 제안한다. 이는 전건부의 언어적 표현이 삼각형 소속함수들을 가지는 기본적인 TSK 퍼지모델에서 체계적으로 유도되어진다. 그리고 유도된 TSK 퍼지모델의 전건부 소속함수들은 GA(Genetic Algorithm)를 이용하여 최적화함으로써 실제 미분방정식에 근사화한다. 아울러 이상의 제안된 방법의 우수성을 모의실험을 통하여 검증한다. Derivation of TSK fuzzy model from nonlinear differential equation is a fundamental issue in the field of theoretical fuzzy control. The method which does not yield affine local differential equations at off-equilibrium points is proposed in this paper. A prototype TSK fuzzy model which has triangular membership functions for linguistic terms of the antecedent part is derived systematically. And then GA is used to modify the membership functions optimally. Simulation results show the validity of the proposed method.
The Evaluations of Sensor Models for Push-broom Satellite Sensor
Lee, Suk-Kun,Chang, Hoon Korean Society of Surveying 2004 Korean journal of geomatics Vol.4 No.1
The aim of this research is comparing the existing approximation models (e.g. Affine Transformation and Direct Linear Transformation) with Rational Function Model as a substitute of rigorous sensor model of linear array scanner, especially push-broom sensor. To do so, this research investigates the mathematical model of each approximation method. This is followed by the assessments of accuracy of transformation from object space to image space by using simulated data generated by collinearity equations which incorporate or depict the physical aspects of linear array sensor.
Adaptive Image Filtering for Scale Space Corner Detection
Shugata Ahmed(슈가타 아흐메드),Cheolkeun Ha(하철근) 제어로봇시스템학회 2012 제어로봇시스템학회 합동학술대회 논문집 Vol.2012 No.7
Gaussian filters are frequently used for scale space based corner detection to remove noise and local variation as many false corners are detected in presence of them. However, an appropriate smoothing scale should be selected for Gaussian filtering method, which is a difficult task. Moreover, edges are smoothed out in this method, which creates difficulty in corner detection. In this paper, we propose an adaptive filtering method based on the anisotropic diffusion for scale space based corner detectors. A new filtering coefficient was developed. Edges and interior regions were filtered separately by selecting appropriate thresholds. Edges were detected by the Canny edge detector and corners were detected by the Affine Resilient Curvature Scale Space (ARCSS) corner detector. Experimental results demonstrated that the proposed adaptive method can detect more corners in less computational time than that of original ARCSS.
ENLARGING THE BALL OF CONVERGENCE OF SECANT-LIKE METHODS FOR NON-DIFFERENTIABLE OPERATORS
Argyros, Ioannis K.,Ren, Hongmin Korean Mathematical Society 2018 대한수학회지 Vol.55 No.1
In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using ${\omega}$-condition and centered-like ${\omega}$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.
Enlarging the ball of convergence of secant-like methods for non-differentiable operators
IOANNISK.ARGYROS,Hongmin Ren 대한수학회 2018 대한수학회지 Vol.55 No.1
In this paper, we enlarge the ball of convergence of a uniparametric family of secant-like methods for solving non-differentiable operators equations in Banach spaces via using $\omega$-condition and centered-like $\omega$-condition meantime as well as some fine techniques such as the affine invariant form. Numerical examples are also provided.
A MODIFIED INEXACT NEWTON METHOD
Huang, Pengzhan,Abduwali, Abdurishit The Korean Society for Computational and Applied M 2015 Journal of applied mathematics & informatics Vol.33 No.1
In this paper, we consider a modified inexact Newton method for solving a nonlinear system F(x) = 0 where $F(x):R^n{\rightarrow}R^n$. The basic idea is to accelerate convergence. A semi-local convergence theorem for the modified inexact Newton method is established and an affine invariant version is also given. Moreover, we test three numerical examples which show that the modified inexact scheme is more efficient than the classical inexact Newton strategy.
A Modified Inexact Newton Method
Pengzhan Huang,Abdurishit Abduwali 한국전산응용수학회 2015 Journal of applied mathematics & informatics Vol.33 No.1
In this paper, we consider a modified inexact Newton method forsolving a nonlinear system $F(x) = 0$ where $F(x):R^n\r R^n$. Thebasic idea is to accelerate convergence. A semi-local convergencetheorem for the modified inexact Newton method is established and anaffine invariant version is also given. Moreover, we test threenumerical examples which show that the modified inexact scheme ismore efficient than the classical inexact Newton strategy.