11 citations · 29 across the 13 of their papers we have counts for
16 papers
Multivariate -normal distributions
Krzysztof Zajkowski
The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformati…
Concentration of norms of random vectors with independent -sub-exponential coordinates
Krzysztof Zajkowski
We present examples of -sub-exponential random variables for any positive . We prove two types of concentration of standard -norms (-norm is the Euclidean norm) of rand…
Bounds on tail probabilities for quadratic forms in dependent sub-gaussian random variables
Krzysztof Zajkowski
We show bounds on tail probabilities for quadratic forms in sub-gaussian non-necessarily independent random variables. Our main tool will be estimates of the Luxemburg norms of suc…
Norms of sub-exponential random vectors
Krzysztof Zajkowski
We discuss various forms of the Luxemburg norm in spaces of random vectors with coordinates belonging to the classical Orlicz spaces of exponential type. We prove equivalent relati…
On norms in some class of exponential type Orlicz spaces of random variables
Krzysztof Zajkowski
A new characterization of the exponential type Orlicz spaces generated by the functions () is given. We define norms for centered random variables belonging…
On the Azuma inequality in spaces of subgaussian of rank random variables
Krzysztof Zajkowski
For let a function if and if . For a random variable let denote $\inf\{c\ge 0 :\; \fora…
On the strong law of large numbers for -subgaussian random variables
Krzysztof Zajkowski
For let if and if . For a random variable let denote $\inf\{a\ge 0:\;\forall_{λ\in\mathbb{R}}\;…
A variational formula on the Cramér function of series of independent random variables
Krzysztof Zajkowski
In [11] it has been proved some variational formula on the Legendre-Fenchel transform of the cumulant generating function (the Cramér function) of Rademacher series with coefficien…
Cramér transform of Rademacher series
Krzysztof Zajkowski
A variational formula for the Cramér transform of series of weighted, independent symmetric Bernoulli random variables (Rademacher series) is given.
Fejer's approximation of continuous functions of unitary operators
Krzysztof Zajkowski
This paper is concerned with a certain aspect of the spectral theory of unitary operators in a Hilbert space and its aim is to give an explicit construction of continuous functions…
A note on the gambling team method
Krzysztof Zajkowski
Gerber and Li in \cite{GeLi} formulated, using a Markov chain embedding, a system of equations that describes relations between generating functions of waiting time distributions f…
On the waiting time till some patterns occur in i.i.d. sequences
Urszula Ostaszewska, Krzysztof Zajkowski
In this paper we present some general solution of the system of linear equations formed by Guibas and Odlyzko in Th.3.3 \cite{Gui}. We derive probabilities for given patterns to be…
Penney's game between many players
Krzysztof Zajkowski
We recall a combinatorial derivation of the functions generating probability of winnings for each of many participants of the Penney's game and show a generalization of the Conway'…
Cramér transform and t-entropy
Urszula Ostaszewska, Krzysztof Zajkowski
t-entropy is the convex conjugate of the logarithm of the spectral radius of a weighted composition operator (WCO). Let be a nonnegative random variable. We show how the Cramér…
Convex conjugates of analytic functions of logarithmically convex functionals
Krzysztof Zajkowski
Let be an analytic function; . We assume that is some logarithmically convex and lower semicontinuous fun…
Covariance matrices of self-affine measures
K. Zajkowski
In this paper we derive a formula for a covariance matrix of any self-affine measure.