## ABSTRACT

This extraordinary compilation is an expansion of the recent American Mathematical Society Special Session celebrating M. M. Rao's distinguished career and includes most of the presented papers as well as ancillary contributions from session invitees. This book shows the effectiveness of abstract analysis for solving fundamental problems of stochas

## TABLE OF CONTENTS

chapter |3 pages

#### M. Rao in this space. As recalled above, a semimartingale F(x, t) is repre

F. If {X, F, t F is a continuous semimartingale, x D, whose local characteristics > 0, then the integral in (53) can be defined with Itô integral is

chapter c|3 pages

#### f. [32, p. 98]) the notion of a regular stationary numerical

K –1, is regular stationary if the component se- are regular and jointly stationary in the sense that the means and n, collections C}, .

chapter |8 pages

#### the results of Bass [2] may be applied because the pre-Hilbert M (x) is a subspace of the Marcinkiewicz space M of sequences in the previous section. To see this, suppose zÎM(x), then

. The theorem of Bass but also that if y and z H (x) N – 1, then µ(z) = (z, 1), m = N – 1 exist for every z

chapter |1 pages

#### if it has the following full rank virile covariance representation t) =

t, 1 j n} . .,Z B let j n,

chapter IV|2 pages

#### 5 A function c : D M is maximal if and only if c(.) H(D) and,

c(.) is a n – m full rank matrix valued function that is maximal, H(t) =

chapter |1 pages

#### the riskless asset or the market portfolio. Similarly, the allocation

pt = [p, ..., is the vector of excess returns p = z – z for

chapter |4 pages

#### In the most general case we can solve the above problem a defined joint distribution of the return vector. However, in the the vectors of risky returns z = [z,...,z]' t = 0, t,...,t are sta-

,... for any j are the deterministic vari- W – x' e where W

chapter |1 pages

#### For instance, see [6], [59],[70], Prediction problems

X, the to X in the in H A}. is of the of the

chapter |1 pages

#### G is either of Type I, Type II, or Type III, as its group von Neumann algebra W*(G) = C*(G)** is of Type I,

G × G is also of Type I, so following Rao [61] we can modify the × such that T

chapter |2 pages

#### of bounded real sequences is denoted by l , with norm || = sup |x|. Note that fÎl, with q < Þ |x| 0, and that l Ì

l. If f = |x| and ||f|| < . l l T