In many applications of the theory of stochastic processes, an important role is played by families of square integrable (second-order) r.v.’s. In this section, we give some basic definitions and prove some fundamental inequalities involving second-order complex-valued r.v.’s.
KeywordsHilbert Space Orthogonal Projection Cauchy Sequence Linear Manifold Complete Orthonormal System
Unable to display preview. Download preview PDF.
- Akhiezer, N.I. and Glazman, I.M. (1963). Theory of Linear Operators in Hilbert Space, Volumes I and II. Frederic Ungar Publishing, Co., New York.Google Scholar
- Natanson, I.P. (1960).Theory of Functions of Real Variables, Volume I and II. Frederic Ungar Publishing, New York.Google Scholar
- Riesz, F. and Sz.-Nagy, B. (1955). Functional Analysis. Frederic Ungar Publishing, New York.Google Scholar
- Royden, H.L. (1968). Real Analysis, 2nd ed. The Macmillan Co., New York.Google Scholar