On the optimal approximation rate of certain stochastic integrals

Optimal Approximation Rate of Certain Stochastic Integrals

Given an increasing function H : [0, 1) → [0,∞) and An(H) := inf τ∈Tn n X i=1 Z ti ti−1 (ti − t)H (t)dt ! 1 2 , where Tn := {τ = (ti) n i=0 : 0 = t0 < t1 < · · · < tn = 1}, we characterize the property An(H) ≤ c √ n , and give conditions for An(H) ≤ c √ nβ and An(H) ≥ 1 c √ nβ for β ∈ (0, 1), both in terms of integrability properties of H . These results are applied to the approximation of cert...

On the approximation of stochastic integrals

Approximation of certain multivariate integrals

A Taylor series approximation to multivariate integrals taken with respect to a multivariate probability distribution is proposed and applied to the computation of multivariate normal probabilities and conditional expectations. The approximation does not require that the multivariate distribution have a structured covariance matrix and, in its simplest form, can be written as the product of uni...

Uniform Approximation for Families of Stochastic Integrals

In view of the extensive use of stochastic integrals and stochastic differential equations in modeling of systems in engineering, and economic systems especially in mathematical finance and other applied problems, it is necessary to find whether there are good approximants to the stochastic integrals and the stochastic differential equations which can be used for simulation purposes. Some work ...

: the effect of sericin levels (silk glue protein) on rate of in vitro maturation, fertilization and culture of sheep oocytes

هدف از آزمایش اول بررسی اثر سطوح مختلف سریسین [0 (control), 0.1, 0.5, 1.0, 2.5 %] افزوده شده به محیط , ivm بر cumulus cell expansion، بلوغ هسته و توسعه متوالی جنین، در گوسفندان نژاد سنجابی در فصل تولید مثلی می باشد. از سرگیری میوز به وسیله خارج شدن اولین پولار بادی اندازه گیری و هم چنین درصد رسیدن جنین های دو سلولی به مرحله کلیواژ و بلاستوسیت نیز به عنوان نشانه ای از میزان شایستگی توسعه اولیه ج...