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

chapter |4 pages

An Appreciation of my teacher, M.M. Rao

ByJ. A. Goldstein

chapter 1001|7 pages

words about Rao

ByM. L. Green

chapter |11 pages

Egoroff, Choquet, etc.).

chapter |2 pages

Reflections on M.M. Rao

ByJerry Uhl

chapter 1|10 pages

Stochastic Analysis and Function Spaces

ByM. M. Rao

chapter C|3 pages

([0, 1]) given by X = {f 1 0

chapter |1 pages

a(0,e) l as

chapter |2 pages

(x,w) = (

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
Byis a in IR with continuous paths, then under the conditions for some = [0 = t < t < ... < t = T]

chapter |2 pages

Medd. Dansk. Vid. Selsk., 34, 1–26.

chapter 2|4 pages

Applications of Sinkhorn balancing to counting problems

ByIsabel Beichl, Francis Sullivan

chapter |1 pages

(D (D

chapter |1 pages

a a , are non-zero,

chapter 3|4 pages

Zakai equation of nonlinear filtering with Ornstein-Uhlenbeck noise: Existence and Uniqueness

ByAbhay Bhatt, Belram Rajput, Jie Xiong

chapter |3 pages

= F.

chapter |4 pages

fµ(hf) +

chapter 4|24 pages

Hyperfunctionals and Generalized Distributions

ByM. Burgin

chapter |15 pages

XYR and K and

chapter |3 pages

HdI . We have HdI Z*, HdI

chapter |3 pages

|g|(z) = var(g, (-, z]) for z × L

chapter |1 pages

|X( , B) – X (B|

chapter |1 pages

Proof: If B

chapter |1 pages

(t,x) a se-

chapter 1|4 pages

= 1

chapter 6|3 pages

Invariant Sets for Nonlinear Operators

ByGiséle Ruiz Goldstein, Jerome A. Goldstein

chapter 8|1 pages

Approximating Scale Mixtures

ByHassan Hamdan, John Nolan

chapter |3 pages

,.. . ,

chapter |7 pages

f(x) =

g/ |) |
By|g(x|

chapter |2 pages

the sums

chapter |2 pages

{x} =

By1|| c

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}, .
ByII.2 A numerical vector sequence z, with K components z for any Z} and {k,k,... ,k

chapter |3 pages

JSx =

chapter |1 pages

f fn R (k,k')

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
Byof the type (3.19). But if the limit for z certainly the limsup exists and so z if y Î H (x) as a limit. | is a continuous invertible linear map in the same manner as Proposition II.4 for and so we omit the proof. (x) = (x, 1) exists form = 0, 1,. Î H(x). is simple and thus omitted, (see for the continuous time case and [5] for a review), gives the connection and cyclostationary sequences. It is the founda- for various representations of stochastic cyclostationary sequences and

chapter |1 pages

G| : C(X × Y) C(X).

chapter 12|15 pages

Connections Between Birth-Death Processes

ByAlan Krinik, Carrie Mortensen, Gerardo Rubino

chapter |1 pages

<...<z

chapter |3 pages

is m(x) for each , j in S = 2, N}.

chapter |5 pages

(bt)

P(t) =
By+...+A

chapter |3 pages

fH(R), we have,

C\\Af\\ = A : X
Byis clear. • a second-order process {xt,t to a normed space X. Let Y be an n — an a to consider the process y = Ax by y(t,w) = , t T, w . First, we have to make sure

chapter |2 pages

Proof. The process x induces a random element

ByE [ (j = E [ (, x

chapter |1 pages

(R x , R

chapter |6 pages

(R ) (s) =

chapter |6 pages

hold:

chapter |1 pages

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

t, 1 j n} . .,Z B let j n,
By: s t, 1 j n} the closure is taken in t as the space of observables of X. be an ] for every {Z( ' is i IV.2 A random process, X, is deterministic if and only if

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) =
By(t) for all t R, and *(•')) = m(• •')I where m(d ) is Lebesgue measure on R, and only if X is purely nondeterministic.

chapter |1 pages

(Y, ) is a stationary dilation of X.

chapter |2 pages

= H (t),

chapter 15|10 pages

Double-Level Averaging on a Stratified Space

ByNatella V. O'Bryant

chapter C|2 pages

**,C > 0, such that

By(af)([X]) ||f||

chapter |1 pages

Gf :=

chapter |1 pages

G+ R

chapter 1|3 pages

2.17 in the case ß = 0 u

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
By+ z,t)W + x'p k = 0,1,2, ...,T – 1 = t, t, ..., t. Therefore, any risk averse investor will choose a strategy the solutions of problem (26) which maximizes his/her

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
By(27) any fixed mean and initial wealth W. The multiperiod portfolio policies the risky assets xt = [x in the riskless return at time t

chapter |1 pages

f is the density of Y. Therefore, when unlimited short selling is

= x'E(z)
Byis a fund separation model whose optimal are given by the optimization problem (19) or equivalently, by the we can solve the optimization

chapter |2 pages

the following allocation problem c (H q))

E(W) - cP(W -VaR) =
Bytry to the

chapter |3 pages

[ ,t,

chapter |2 pages

for any = arg –

chapter |1 pages

Q ] =

chapter |3 pages

z= [z,..., is

chapter 17|5 pages

Computations for Nonsquare Constants of Orlicz spaces

ByZ D. Ren

chapter |2 pages

CF (t) exists and =

chapter |2 pages

)) = J(L

chapter |6 pages

F(1) F(1/2)

chapter |1 pages

T > 0, let T–| |/2 = E(XX )dt

chapter |2 pages

(t, . . . ,t

chapter |15 pages

(i)– to to it

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
Byby Niemi [45],[46],[48]. the prediction and filtering problems as follows. an asymptotically stationary process on {X : s a in the of the in

chapter |4 pages

For a,..., a C and t,..., t 0,

chapter |2 pages

f ( ) , = lim

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
Byin §3.1 as follows. Let G be of Type I. We call the continuous process {X(t), Î G} strongly harmonizable if K Î B(G), so X is strongly harmonizable a measurable mapping T on is a

chapter |1 pages

K( t,t) =

chapter |1 pages

* (x) ...

chapter V|2 pages

–region are met. It remains

chapter 20|8 pages

Doubly Stochastic Operators and the History of Birkhoff s Problem 111

BySheila King, Ray Shiflett

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
ByLet P= (p) be a given infinite stochastic matrix and let Tf = fP let Tf = fP = T is positive and linear. It follows that ||Tf|| = all terms are positive. So ||Tf|| ||T|| 1. Finally, from absolute convergence, STf = S (S

chapter |3 pages

Proof: Assume S: l

chapter |3 pages

+ II

chapter |6 pages

U 0 = see that f(W)

Bythe way W was expanded the countably infinite to the uncountable case. Until now, the study has to work with operators induced by matrices, and stochastic prop- in terms of finite or infinite row and column sums. In the

chapter 21|3 pages

Classes of Harmonizable Isotropic Random Fields

ByRandall J. Swift

chapter |4 pages

' the representation of the covariance becomes ( t) = 2 J ( ) = r s – dF(

s – dF(
Byis the representation of a stationary isotropic covariance obtained by in spherical-polar form for the covariances was also given by Swift in

chapter |1 pages

(–1) · (

chapter |17 pages

|| x ||,

chapter |1 pages

4k (V + ± 4kk

chapter |2 pages

w(x,y,t) = Cl(kt

chapter |7 pages

, ) = 0, F(