Let y ≡ y(2d) = {yi}i∈Zn+ ,|i|62d denote a real n-dimensional multisequence of degree 2d, y0 > 0. Let Ly : R2d[x1, . . . , xn] 7→ R denote the Riesz functional, defined by Ly(∑|i|62d aix i) = ∑ aiyi, and let Md(y) denote the corresponding moment matrix. Positivity of Ly plays a significant role in the Truncated Moment Problem and in the Polynomial Optimization Problem, but concrete conditions f...

where a < 0 < b and 0 < p < 1 represents the probability of downword jumps and q = 1− p is the probability of upward jumps. The set indicator function is I{S} for set S. The mean of Q is μj = 1 2 (pa + qb) and the variance of Q is σ j = pq 4 (b− a) + pa2+qb2 12 . The third central moment of Q is M (3) j ≡ E[(q − μj)] = pq 4 (b − a)(aq + bp) and The fourth central moment of Q is M (4) j ≡ E[(q−μ...

In this paper we present a simple control variate method, for options pricing under stochastic volatility models by the risk-neutral pricing formula, which is based on the order moment of the stochastic factor Yt of the stochastic volatility for choosing a non-random factor Y (t) with the same order moment. We construct the control variate using a stochastic differential equation with a determi...

In this work we suggest a simple mathematical model for the dynamics of the population of children and adolescents without problematic behavior (criminal activities etc.). This model represents a typical population growth equation but with time dependent (linearly decreasing) population growth coefficient. Given equation admits definition of the half-life time of the non-problematic children be...

We studied the between-therapist reliability and the validity of four instruments in measuring lumbar spine curvature and pelvic tilt. The four instruments and their measurements were 1) a tape measure to measure the change in lumbar curvature during trunk flexion; 2) a gravity goniometer to measure pelvic angle and lumbar curvature during stance, trunk flexion, and trunk extension; 3) a parall...

Relatively little is known about the ability of numerical methods for stochastic differential equations (SDEs) to reproduce almost sure and small-moment stability. Here, we focus on these stability properties in the limit as the timestep tends to zero. Our analysis is motivated by an example of an exponentially almost surely stable nonlinear SDE for which the Euler–Maruyama (EM) method fails to...

A recursive least square RLS algorithm for estimation of vehicle sideslip angle and road friction coefficient is proposed. The algorithm uses the information from sensors onboard vehicle and control inputs from the control logic and is intended to provide the essential information for active safety systems such as active steering, direct yaw moment control, or their combination. Based on a simp...

We introduce three differentially-private algorithms that approximates the 2nd-moment matrix of the data. These algorithm, which in contrast to existing algorithms output positive-definite matrices, correspond to existing techniques in linear regression literature. Specifically, we discuss the following three techniques. (i) For Ridge Regression, we propose setting the regularization coefficien...

A Moment Ratio Estimator is proposed for the parameters of an Autoregressive (AR) model of the error in an Ordinary Least Squares (OLS) linear regression. Although it is computed from the conventional residual autocorrelation coefficients, it greatly reduces their bias, and provides corrected standard errors with far less bias and confidence intervals with far less size distortion than conventi...

We show that very large bandwidths on fading multipath channels cannot be effectively utilized by spread-spectrum systems that (in a particular sense) spread the available power uniformly over both time and frequency. The approach is to express the input process as an expansion in an orthonormal set of functions each localized in time and frequency. The fourth moment of each coefficient in this...