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

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The lattice and cover structure of atoms, 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

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Shan-Hwei Nienhuys-Cheng,Roland Wolfral 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

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The lattice and cover structure of atoms,ems with scalar normalizations have been much investigated and form the basis of classical probability theory. At the same time, it has not been until recently when studying operator normalizations (especially in the framework of almost sure convergence) began, though these normalizations are more a

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Lecture Notes in Computer Scienceiterated 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

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