Mariusz Mirek

activity

20092026

most citedA bootstrapping approach to jump inequalities and their applications

29 citations · 181 across the 37 of their papers we have counts for

collaborators

Showing math.PRShow all

5 papers · 1 filter

math.PR2012★ 24 cited

Heavy tailed solutions of multivariate smoothing transforms

Dariusz Buraczewski, Ewa Damek, Sebastian Mentemeier +1

Let $N > 1$ be a fixed integer and $(C_{1}, ..., C_{N}, Q)$ a random element of $G L (d, R)^{N} x R^{d}$ . We consider solutions of multivariate smoothing transforms, i.e. random variables $R…

math.PR2011

On fixed points of a generalized multidimensional affine recursion

Mariusz Mirek

Let $G$ be a multiplicative subsemigroup of the general linear group $\Gl(\mathbb{R}^d)$ which consists of matrices with positive entries such that every column and every row conta…

math.PR2011★ 6 cited

Convergence to stable laws for multidimensional stochastic recursions: the case of regular matrices

Ewa Damek, Sebastian Mentemeier, Mariusz Mirek +1

Given a sequence $(M_{n}, Q_{n})_{n \geq 1}$ of i.i.d.\ random variables with generic copy $(M, Q) \in G L (d, R) \times R^{d}$ , we consider the random difference equation (RDE) $$ R_{n}…

math.PR2010

Asymptotics of stationary solutions of multivariate stochastic recursions with heavy tailed inputs and related limit theorems

Dariusz Buraczewski, Ewa Damek, Mariusz Mirek

Let $Φ_{n}$ be an i.i.d. sequence of Lipschitz mappings of $R^{d}$ . We study the Markov chain ${X_{n}^{x}}_{n = 0}^{\infty}$ on $R^{d}$ defined by the recursion $X_{n}^{x} = Φ_{n} (X_{n - 1}^{x})$ , $n\…

math.PR2009★ 1 cited

Heavy tail phenomenon and convergence to stable laws for iterated Lipschitz maps

Mariusz Mirek

We consider the Markov chain ${X_{n}^{x}}_{n = 0}^{\infty}$ on $R^{d}$ defined by the stochastic recursion $X_{n}^{x}=\p_{θ_{n}}(X_{n-1}^{x})$, starting at $x \in R^{d}$ , where $θ_{1}, θ_{2}…