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The relationship between quadratic variation for compound renewal processes and M-Wright functions is discussed. The convergence of quadratic variation is investigated both as a random variable (for given t) and as a stochastic process.

Random Oper. Stoch. Equ. 19 (2011), 197–216 DOI 10.1515/ROSE.2011.012 © de Gruyter 2011 Estimation of the long memory parameter in stochastic volatility models by quadratic variations Ionuţ Florescu and Ciprian A. Tudor Communicated by V. L. Girko Abstract. We consider a stochastic volatility model where the volatility process is a frac- tional Brownian motion. We estimate the memory parameter of the volatility from discrete observations of the price process. We use criteria based on Malliavin calculus in order to characterize the asymptotic normality of the

motion, Stochastic Process. Appl. 116 (2006), 5, 830–856. Russo F. Tudor C. A. On bifractional Brownian motion Stochastic Process. Appl. 116 2006 5 830 856 14 M. Taqqu, Convergence of integrated processes of arbitrary Hermite rank, Z. Wahrsch. Verw. Gebiete 50 (1979), 1, 53–83. Taqqu M. Convergence of integrated processes of arbitrary Hermite rank Z. Wahrsch. Verw. Gebiete 50 1979 1 53 83 15 C. Tudor, Berry–Esséen bounds and almost sure CLT for the quadratic variation of the sub-fractional Brownian motion, J. Math. Anal. Appl. 375 (2011), 2, 667–676. Tudor C. Berry

Existence and Continuity of the Quadratic Variation of Strong Martingales Nikos E. Frangos and Peter Imkeller Abstract We prove the existence (in the sense of Lq convergence) of L ι -bounded strong martingales. The proof is through stochastic inteigrals with respect to strong martingales. The continuity is an easy consequence of the fact that the Q.V. of a strong martingale is equal to the Q.V. of either of the one parameter 'marginal' martingales. Let Af be a strong martingale. We assume that Μ is regular (see Walsh [12]). By one parameter results we

Random Oper, and Stoch. Equ., Vol. 6, No. 2, pp. 183-199 (1998) ( VSP 1998 Quadratic variation and Riemann sums for the generalized multiple Skorokhod integral Rosario DELGADO and Maria JOLIS Departament de Matemätiques, Edifici C Universität Autonoma de Barcelona, 08193 Bellaterra, Barcelona, Spain. Received for ROSE March 4, 1997 Abstract—We give two approximations by Riemann sums for the generalized multiple Skorokhod- type integral and also obtain several results for this integral as a process, such as an orthogonality property, its quadratic variation and a

P r o b . T h e o r y a n d M a t h . S t a t . , Vo l . 2 , p p . 1 8 1 - 1 9 2 B . G r i g e l i o n i s ti a / . ( E d s . ) 1 9 9 0 V S P / M o k s l a s TWO-PARAMETER STRONG MARTINGALES: INEQUALITIES FOR QUADRATIC VARIATION A N D SOME DECOMPOSITIONS Yu.S.MISHURA and A.A.GUSHCHIN Kiev University, 252601 Kiev, Ukraine, USSR Steklov Mathematical Institute, Vavilova 42, 117966 Moscow GSP-1, USSR ABSTRACT The paper contains generalizations of Burkholder—Davis—Gundy inequalities for strong two parameter martingales with discrete and continuous

1 Introduction In this paper, we discuss the properties of third and fourth moment variations and their realized versions of financial asset returns. The realized third and fourth moments are defined based on quadratic variation methods as extensions of the definition of the realized variance which is a high-frequency data based estimator for the variance of asset returns. The realized third and fourth moments are unbiased estimators of the third and fourth moments of return, respectively, under the martingale assumption of the return process. The third and

Monte Carlo Methods and Appl., Vol. 13, No. 2 (2007), pp. 99–116 DOI 10.1515 / MCMA.2007.006 c© de Gruyter On a real-time scheme for the estimation of volatility Shigeyoshi Ogawa and Koji Wakayama Abstract. We are interested in the numerical scheme for the estimation of the volatility of a given price process St, which in the Black-Sholes paradigm is supposed to follow the Itô type stochastic differential equation. Keywords. Volatility, Black-Scholes paradigm, Fourier series techniqie, quadratic variation scheme. AMS classification. 65C05, 65C30. 1. Introduction

valid even if we add jump processes of finite or infinite activity to the underlying diffusion process. These statistics extend the quadratic variational approach and are related to the concept of multipower variation, which is used in the problem of estimating the integrated volatility. Keywords. Spot volatility, central limit theorem, robustness, jump process, microstructure noise. AMS classification. 62G05, 60J60, 60J75. 1. Introduction We consider a d-dimensional stochastic process (X(t))t≥0 defined on the filtered prob- ability space (Ω,F , (Ft)t≥0,P) given by dX

An efficient C0 continuous finite element (FE) model is developed based on a combined theory (refine higher order shear deformation theory (RHSDT) and least square error (LSE) method) for the static analysis of a soft core sandwich plate. In this (RHSDT) theory, the in-plane displacement field for the face sheets and the core is obtained by superposing a global cubically varying displacement field on a zig-zag linearly varying displacement field with a different slope in each layer. The transverse displacement assumes to have a quadratic variation within the core and it remains constant in the faces beyond the core. The proposed model satisfies the condition of transverse shear stress continuity at the layer interfaces and the zero transverse shear stress condition at the top and bottom of the sandwich plate. The nodal field variables are chosen in an efficient manner to circumvent the problem of C1 continuity requirement of the transverse displacements. In order to calculate the accurate through thickness transverse stresses variation, the Least Square Error (LSE) method has been used at the post processing stage. The proposed combined model (RHSDT and LSE) is implemented to analyze the laminated composites and sandwich plates. Many new results are also presented which should be useful for future research.