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Theory and applications of probability and stochastic processes: e.g. central limit theorems, large deviations, stochastic differential equations, models from statistical mechanics, queuing theory.

1 vote
1 answer
282 views

Exponential upper bounds for sums of martingale differences

Let $(X_{i})_{i\geq 1}$ be a sequence of centered real-valued martingale-differences with respect to some filtration $(\mathcal{F}_{i})_{i \geq 1}$. Define $S_{n} = \sum_{i=1}^{n}X_{i}$ and $\Sigma^{2 …
2 votes
0 answers
79 views

Constructing weakly-dependent process with certain decay rate of dependency coefficients

Let $(X_{t})_{t \in \mathbb{N}}$ be a real-valued stationary stochastic process over probability $(\Omega,\mathcal{F},\mathbb{P})$, such that for $p\geq 2$, $X_{t} \in L_{p}(\mathbb{P})$ and it holds: …
3 votes
1 answer
152 views

Question on example 3.0.1 in Yurinsky's book "Sums and Gaussian vectors"

Good day to All. Let $S_{1,n} = \sum_{i=1}^{n}\xi_{i}$, where $(\xi_{i})_{i \in \mathbb{N}}$ be independent RV with values in some Banach space. On pages 79-80 in this book author provides an examp …