Based on a sequence of discretized American option price processes under the multinomial model proposed by Maller, Solomon and Szimayer [12], the sequence converges to the counterpart under the original Lévy process in distribution for almost all time. By adapting Skorokhod representation theorem, a new sequence of approximating processes with the s ame laws with the multinomial tree model defi...

Abstract In the present article we consider a type of matrices stemming in context numerical approximation distributed order fractional differential equations (FDEs). From one side they could look standard, since are real, symmetric and positive definite. On other hand cause specific difficulties which prevent successful use classical tools. particular associated matrix-sequence, with respect t...

In this paper we extend the contraction mapping method to prove various existence and uniqueness properties of (self-similar) random fractal measures, and establish exponential convergence results for approximating sequences defined by means of the scaling operator. For this purpose we introduce a version of the Monge Kantorovich metric on the class of probability distributions of random measur...

We present an algorithm for approximating a given open polygonal curve with a minimum number of circular arcs. In computer-aided manufacturing environments, the paths of cutting tools are usually described with circular arcs and straight line segments. Greedy algorithms for approximating a polygonal curve with curves of higher order can be found in the literature. Without theoretical bounds it ...

In many situations, there is a need to approximate a sequence of probability measures over a growing product of finite spaces. Whereas it is in general possible to determine analytic expressions for these probability measures, the number of computations needed to evaluate these quantities grows exponentially thus precluding real-time implementation. Sequential Monte Carlo techniques (SMC), whic...

The Lanczos algorithm for tridiagonalizing a given matrix A generates a sequence of approximating matrices A, that can naturally be obtained as restrictions to subspaces. The eigenvalues of these approximating matrices are well known to be good approximations to the extreme eigenvalues of A. In this paper we produce explicit formulas for the characteristic polynomials of the A,, in terms of the...