On the Mixed Modulus of Smoothness and a Class of Double Fourier Series

MSC 2010: 42A32; 42A20

A New Algorithm for Monte Carlo for American Options

2000 Mathematics Subject Classification: 91B28, 65C05.

On generalized orlicz sequence spaces of Fourier coefficients for trigonometric gap series. I.

We investigate the operator associating with a function fєLp2π, 1Fourier coefficients of ƒ with respect to a trigonometric gap system, as well as an operator from a modular space X ρs(ϕ) to the generalized Orlicz sequence space lϕ.

Geometric Stable Laws Through Series Representations

Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study the asymptotic behavior of the partial sum process SN (t) = ⅀( i=1 ... [N t] ) Xi , and derive series representations of the limiting geometric stable process and the corresponding stochastic integral. We also obtain strong invariance principles for stable and geometric stable laws.

Solutions of Analytical Systems of Partial Differential Equations

In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).

An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators

2000 Mathematics Subject Classification: 42B10, 43A32.

Cauchy-Type Problem for Diffusion-Wave Equation with the Riemann-Liouville Partial Derivative

2000 Mathematics Subject Classification: 35A15, 44A15, 26A33

On Hankel Transform of Generalized Mathieu Series

Mathematics Subject Classification: Primary 33E20, 44A10; Secondary 33C10, 33C20, 44A20

Multiplicative Systems on Ultra-Metric Spaces

AMS Subj. Classification: MSC2010: 42C10, 43A50, 43A75

An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative

Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.

Zeros of Sequences of Partial Sums and Overconvergence

2000 Mathematics Subject Classification: 30B40, 30B10, 30C15, 31A15.