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12 papers
A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations
Danijel Krizmanic
In this article we derive a self-normalized functional limit theorem for strictly stationary linear processes with i.i.d. heavy-tailed innovations and random coefficients under the…
A functional limit theorem for self-normalized partial sum processes in the topology
Danijel Krizmanic
For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index and weak dependence conditi…
Joint functional convergence of partial sums and maxima for moving averages with weakly dependent heavy-tailed innovations and random coefficients
Danijel Krizmanic
For moving average processes with random coefficients and heavy-tailed innovations that are weakly dependent in the sense of strong mixing and local dependence condition we st…
Skorokhod convergence of maxima of multivariate linear processes with heavy-tailed innovations and random coefficients
Danijel Krizmanic
We derive functional convergence of the partial maxima stochastic processes of multivariate linear processes with weakly dependent heavy-tailed innovations and random coefficients.…
A note on joint functional convergence of partial sum and maxima for linear processes
Danijel Krizmanic
Recently, for the joint partial sum and partial maxima processes constructed from linear processes with independent identically distributed innovations that are regularly varying w…
Joint functional convergence of partial sum and maxima for linear processes
Danijel Krizmanic
For linear processes with independent identically distributed innovations that are regularly varying with tail index , we study functional convergence of the joint par…
On joint weak convergence of partial sum and maxima processes
Danijel Krizmanic
For a strictly stationary sequence of random variables we derive functional convergence of the joint partial sum and partial maxima process under joint regular variation with index…
Weak convergence of multivariate partial maxima processes
Danijel Krizmanić
For a strictly stationary sequence of --valued random vectors we derive functional convergence of partial maxima stochastic processes under joint regular variat…
Functional weak convergence of partial maxima processes
Danijel Krizmanić
For a strictly stationary sequence of nonnegative regularly varying random variables we study functional weak convergence of partial maxima processes $M_{n}(t) = \bigvee_…
On the convergence for partial sum processes with a reduced number of jumps
Danijel Krizmanic
Various functional limit theorems for partial sum processes of strictly stationary sequences of regularly varying random variables in the space of cadlag functions with on…
Weak convergence of partial maxima processes in the topology
Danijel Krizmanić
It is known that for a sequence of independent and identically distributed random variables the regular variation condition is equivalent to weak convergence of partial m…
A Multivariate Functional Limit Theorem in Weak M1 Topology
Bojan Basrak, Danijel Krizmanić
We show a new functional limit theorem for weakly dependent regularly varying sequences of random vectors. As it turns out, the convergence takes place in the space of R^d valued c…