Titlebook: Asymptotic Behaviour of Linearly Transformed Sums of Random Variables; Valery Buldygin,Serguei Solntsev Book 1997 Springer Science+Busines

paragon

https://doi.org/10.1007/978-0-387-35608-2llation theorem due to K.Itô and M.Nisio and reduces the problem of sample continuity of almost all sample paths of Gaussian processes to that of the almost sure convergence to zero of Gaussian sequences. Even though the statement on reduction is proved under fairly general assumptions on the parame

FISC

AFFIX

使迷醉

Series of independent random elements of strong and weak almost sure convergence of series of independent symmetric summands (a generalization of the Itô-Nisio theorem) is considered in Section 1.3. In Section 1.4, a theorem is established to relate convergence of series of independent symmetric summands with concentration of distribut

fledged

Linear transformations of independent random elements and series in sequence spacesral framework. The sequences resulting from these transformations may be represented as series of independent random elements in different sequence spaces. The properties of almost all sample paths of the underlying sequences (such as convergence, convergence to zero, boundedness, etc.) define the c

沐浴

Flagging

Operator-normed sums of independent identically distributed random vectorshat the terms are identically distributed not only makes much more simple formulations of the main statements, but also enables revealing some interesting effects. First of all, this applies to Sections 4.3 and 4.4. In Section 4.3, we prove statements on equivalence of scalar and operator normalizat

nonsensical

Continuity of sample paths of Gaussian Markov processesof continuity of Markov processes is complemented by an entropy criterion which gives evidence that the necessary conditions of continuity of Gaussian processes due to V.Sudakov are sufficient for continuity of Gaussian Markov processes. This problem is considered in Section 6.4 which logically acco

Radiation

The interplay between strong and weak limit theorems for sums of independent random variablesiterated logarithm in the framework of identically distributed summands. In other words, the principal problem is posed of whether a generalized LIL may take place. The following result is well-known to be true for independent identically distributed random variables; this result associates the poss

absolve

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