کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4668813 | 1346078 | 2014 | 17 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Identification of a noncausal Itô process from the stochastic Fourier coefficients
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Identification of a noncausal Itô process from the stochastic Fourier coefficients Identification of a noncausal Itô process from the stochastic Fourier coefficients](/preview/png/4668813.png)
چکیده انگلیسی
Let Xt be a noncausal Itô process of Skorokhod type driven by the Brownian motion W., that is, a stochastic process of the form dXt=b(t,Ï)dt+a(t,Ï)dWt where the term a(â
)dWt is understood as Skorokhod integral. For such an Itô process Xt we consider the Fourier coefficient Fn(dX) of the differential dXt by Fn(dX)=â«01en(t)¯dXt, en(t)=exp(2Ïâ1nt) (nâZ) and we are concerned with the elementary question: whether we can identify the two parameters a(â
,Ï), b(â
,Ï) from the complete set of the stochastic Fourier coefficients {Fn(dX),nâZ}. In this note we study this problem in a framework of noncausal calculus, as we did in the previous articles (Ogawa, 2013; Ogawa and Uemura, in press), and we give an affirmative answer with a concrete scheme for the reconstruction of the parameters a(â
,Ï), b(t,Ï). Our result will give another light to the theoretical background of the method of Fourier series for the volatility estimation proposed by P. Malliavin et al. (Malliavin and Mancino, 2002; Malliavin and Thalmaier, 2009).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Bulletin des Sciences Mathématiques - Volume 138, Issue 1, JanuaryâFebruary 2014, Pages 147-163
Journal: Bulletin des Sciences Mathématiques - Volume 138, Issue 1, JanuaryâFebruary 2014, Pages 147-163
نویسندگان
Shigeyoshi Ogawa, Hideaki Uemura,