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.
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 quadraticvariation of the sub-fractional Brownian motion,
J. Math. Anal. Appl. 375 (2011), 2, 667–676.
Tudor C. Berry
Existence and Continuity of the QuadraticVariation 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 ). By one
parameter results we
Random Oper, and Stoch. Equ., Vol. 6, No. 2, pp. 183-199 (1998)
( VSP 1998
Quadraticvariation 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 quadraticvariation 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
MARTINGALES: INEQUALITIES FOR
QUADRATICVARIATION A N D
Yu.S.MISHURA and A.A.GUSHCHIN
Kiev University, 252601 Kiev, Ukraine, USSR
Steklov Mathematical Institute, Vavilova 42, 117966 Moscow GSP-1, USSR
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 quadraticvariation 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
valid even if we add jump processes of finite
or infinite activity to the underlying diffusion process. These statistics extend the quadraticvariational 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
AMS classification. 62G05, 60J60, 60J75.
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
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.