Quantum stochastic calculus on interacting Fock spaces: semimartingale estimates and stochastic integral

Hyers-Ulam Stability of Differentiation Operator on Hilbert Spaces of Entire Functions

“…About the function spaces, we recommend the research papers [18,19]. For the sake of coherency we recall a few basic definitions, notions, and theorems from [18], and we also give some typical examples; in particular Fock space in these examples is a very important tool for quantum stochastic calculus in the case of quantum probability (see [20][21][22]).…”

On Fractional Brownian Motion and Wavelets

“…Conversely, the use of wavelet analysis allows us to gain new insight into the study of fractional Brownian motion [e.g., formula (24) in Lemma 4 (Sect. 3)]. This is a correspondence between points in a certain infinite-dimensional unitary group on the one side, and a family of representations of the Cuntz algebras on the other.…”

“…Later papers on this theme include [3][4][5][6] and references therein, to mention only a few. We will have occasion to use the following references regarding C * -algebras [7][8][9][10][11][12][13][14][15][16]; on multiresolutions and wavelets [4,10,[17][18][19][20][21][22][23][24][25][26][27][28][29]; and results from harmonic analysis, [30][31][32][33][34][35][36][37][38]; on Hilbert and reproducing kernels [3,[39][40][41][42]; on Markov measures [1,2,5,6,11,[43][44]…”