Functional limit theorems for \(C\)-\(R\) increments of \(l^p\)-valued Wiener processes in the Hölder norm (Q2581174)

Let \(W_1(t)\), \(W_2(t),\dots\), \(t\in[0,\infty)\), be independent standard Wiener processes and for \(e\in l^p\) denote \(e\cdot W(t)= (e_1W_1(t),e_2W_2(t),\dots)\) an \(l^p\)-valued Wiener process. Some functional laws of iterated logarithm for increments of \(e\cdot W(t)\) in the Hölder norm in the space \(C_0[0,1]^\infty\) are proved. To get the results a large deviation technique is applied.