In the general geometric asset price model, the asset price P (t) at time t satisfies the relation P (t) = P0 · eα·f(t)+σ·F (t) , t ∈ [0, T ], where f is a deterministic trend function, the stochastic process F describes the random fluctuations of the market, α is the trend coefficient, and σ denotes the volatility. The paper examines the problem of optimal trend estimation by utilizing the con...

Recent theoretical studies of chaotic scattering have encounted ensembles of random matrices in which the eigenvalue probability density function contains a one-body factor with an exponent proportional to the number of eigenvalues. Two such ensembles have been encounted: an ensemble of unitary matrices specified by the so-called Poisson kernel, and the Laguerre ensemble of positive definite ma...

It is well known that subspaces of the Hardy space over the unit disk which are invariant under the backward shift occur as the image of an observability operator associated with a discrete-time linear system with stable state-dynamics, as well as the functional-model space for a Hilbert space contraction operator. We discuss two multivariable extensions of this structure, where the classical H...

and Applied Analysis 3 Since i ∞ i=1 is dense in [0, 1], (Lu)(x) = 0, which implies that u ≡ 0 from the existence of L. Using reproducing kernel property, it can be written as i (x) = i (y) , x (y)⟩ = ⟨(L ∗ i (x) , x (y)⟩ = i (y) , x (y)⟩

The notion of reproducing kernel Hilbert space (RKHS) has emerged in system identification during the past decade. In resulting framework, impulse response estimation problem is formulated as a regularized optimization defined on an infinite-dimensional RKHS consisting stable responses. consequent well-defined under central assumption that convolution operators restricted to are continuous line...

A scheme of construction of integral representations on spaces of analytic functions is presented. The scheme gives a general explicit formula for the reproducing kernels. Its construction is based on symmetry groups of systems of differential equations, which define the “analytic” property of functional spaces. Given examples offer a new view on the classical results on this problem

This paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series.An iterative method is given to obtain the approximate solution.The conver...

This paper is concerned with a technique for solving Volterra integro-dierential equationsin the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernelmethod, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series. An iterative method is given toobtain the...

This tutorial paper discusses a number of classical interpolation results from the theory of Hardy spaces, and stresses the role played by reproducing kernels. Next, the reproducing kernel thesis is presented in several different contexts. Some basics of the theory of linear systems are described, leading into two applications of the abstract results: the first is in the recovery of functions f...

All solutions of a tangential interpolation problem for contractive multipliers between two reproducing kernel Hilbert spaces of analytic vectorvalued functions are characterized in terms of certain positive kernels. In a special important case when the spaces consist of analytic functions on the unit ball of Cd and the reproducing kernels are of the form (1 − 〈z, w〉−1)Ip and (1−〈z,w〉)−1Iq, the...