J. David Mason

Operator-self-similar processes in a finite-dimensional space

A general representation for an operator-self-similar process is obtained and its class of exponents is characterized. It is shown that such a process is the limit in a certain sense of an operator-normed process and any limit of an operator-normed process is operator-self-similar.

Operator-self-similar stable processes

Operator-self-similar processes are studied and several examples of operator-self-similar and stable (in the ordinary sense or in the sense of operator-stable) processes are constructed. Limit theorems for such processes are also shown.

The depression of T lymphocytes after trauma

Abstract The T lymphocyte count is usually depressed during the first 24 to 48 hours after trauma or operation. It usually starts to return to normal levels by the fifth day after injury. The degree of depression is related to the severity of the injury. Acute infection appears to trigger this depression prior to operative treatment. This transient depression may be a normal physiologic event associated with the stress of trauma or infection.

Variational sums for additive processes

Let X(t), 0 c t c T, be an additive process, and let Xnk be the kth increment of X(t) associated with the partition rIn of [0, T]. Assume IIR, II -n| 0. Let f3 be the Blumenthal-Getoor index of X(T) and let 2 _ y > /8. When the partitions are nested, k IXkly converges a.s. to I {IJ(s)IT: 0 _ s _ T}, where J(s) is the jump of X(t) at s. This convergence also holds when the partitions are not nested provided either X(t) has stationary increments or 1 _ y > ,B. This extends a result of P. W. Millar and completes a result of S. M. Berman.

The effects of prolonged coffee intake on genetically identical mice.

Abstract C57BL6J mice were fed coffee over a prolonged period of time (adult life). They had a statistically significant decrease in longevity as compared to the genetically identical controls. The coffee fed animals developed a markedly deteriorated physical condition and lower weights despite the fact that they consumed as much or more food and fluid than the water fed controls.

Operator — Stable distributions with independent marginals

SummaryLet Μ be a full operator-stable probability measure over a finite dimensional real inner product space V. Necessary and sufficient conditions are obtained for Μ to have independent univariate marginals with respect to some basis of V. These essentially amount to the statement that the support of the Lévy spectral measure is a subset of the union of one-dimensional subspaces of V determined by the vectors in a basis of the subspace of V spanned by the support of the non-Gaussian component. A representation for an exponent of such a Μ is also given.