The quadratic variation of a Brownian motion indexed by a nonempty closed subset of the reals, i.e. a time scale, is investigated and examples are given for various time scales to illustrate the result.doi:10.1
这里的dz^2=dt 表示是的brownian motion的quadratic variation等于t建议找本stochastic calculus的书看看 ...
Volatility of VarianceSelf Decomposable LawsSato Lévy MixturesTime changes of Brownian motion impose restrictive jump structures in the motion of asset prices. Quadratic variations also depart from time changes. Joint LaplMadan, Dilip B.Wang, King...
For financial assets whose best quoted prices are almost always revised by the minimum price tick, this paper proposes an estimator of quadratic variation which is robust to microstructure effects. It compares the number of alternations, where quotes are revised back to their previous price, to the...
increases as a result of magnification in nanoparticles. Zainal et al.33contemplated hybrid nanofluid under the effect of stagnation point and suction effect moving subjected to a flat plate and creating that the heat transition of the liquid magnifies as a result of a positive variation in suction...
As mentioned in Bensoussan, Sung, Yam, and Yung (2014), Elliott, Li, and Ni (2013) and Yong (2013), the purpose of studying stochastic optimal control for MFSDEs is to analyze macroscopic behavior of large-scale interacting multi-agent systems and reduce variation of random effects on the...
mixed fractional Brownian motionMalliavin calculuslocal timefractional Itô formulaLet W=λB+νBH${W}=\\\lambda B+u B^{H}$ be a mixed-fractional Brownian motion with Hurst index 0 doi:10.1186/s13660-016-1254-2Han GaoKun HeLitan YanSpringerOpenJournal of Inequalities and Applications...
Fractional Brownian motionQuadratic variationRandomized periodogramDzhaparidze and Spreij (Stoch Process Appl, 54:165–174, ) showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of...
(2012). The quadratic variation of Brownian motion on a time scale. Statist. Probab. Lett., 82(9), 1677-1680. http://dx.doi.org/10.1016/j.spl.2012.05.008D. GROW, S. SANYAL, The quadratic variation of Brownian motion on a time scale, Statistics & Probability Letters 82.9 (2012), ...
motion(sbBm) of dimension 1, with indices H∈(0,1) and K∈(0,1]. By using the Malliavin calculus and the Stein's method, we mainly obtain Berry-Esséen bounds and prove the almost sure central limit theorem (ASCLT) for the quadratic variation of the sub-bifractional Brownian motion....