179 citations · 208 across the 27 of their papers we have counts for
34 papers
Fock structure of complete Boolean algebras of type I factors and of unital factorizations
Matija Vidmar
The factorizable vectors of a complete Boolean algebra of type I factors, acting on a separable Hilbert space, are shown to be total, resolving a conjecture of Araki and Woods. En…
Stationary local random countable sets over the Wiener noise
Matija Vidmar, Jon Warren
The times of Brownian local minima, maxima and their union are three distinct examples of local, stationary, dense, random countable sets associated with classical Wiener noise. Be…
Continuous-state branching processes with collisions: first passage times and duality
Clément Foucart, Matija Vidmar
We introduce a class of one-dimensional positive Markov processes generalizing continuous-state branching processes (CBs), by taking into account a phenomenon of random collisions.…
Complete monotonicity of time-changed Lévy processes at first passage
Matija Vidmar
We consider the class of (possibly killed) spectrally positive Lévy process that have been time-changed by the inverse of an integral functional. Within this class we characterize…
Some characterizations for Markov processes at first passage
Matija Vidmar
Suppose is a Markov process on the real line (or some interval). Do the distributions of its first passage times downwards (fptd) determine its law? In this paper we treat some…
Continuous-state branching processes with spectrally positive migration
Matija Vidmar
Continuous-state branching processes (CSBPs) with immigration (CBIs), stopped on hitting zero, are generalized by allowing the process governing immigration to be any Lévy process…
A potpourri of results in the general theory of stochastic noises
Matija Vidmar
The objects under inspection, on a given probability space, are noise(-type) Boolean algebras -- distributive non-empty sublattices of the lattice of all complete sub--fields, w…
A nonclassical solution to a classical SDE and a converse to Kolmogorov's zero-one law
Matija Vidmar
For a discrete-negative-time discrete-space SDE, which admits no strong solution in the classical sense, a weak solution is constructed that is a (necessarily nonmeasurable) non-an…
Some harmonic functions for killed Markov branching processes with immigration and culling
Matija Vidmar
For a continuous-time Bienaymé-Galton-Watson process, , with immigration and culling, as an absorbing state, call the process that results from killing at rate $q\…
On laws exhibiting universal ordering under stochastic restart
Matija Vidmar
For each of (i) arbitrary stochastic reset, (ii) deterministic reset with arbitrary period, (iii) reset at arbitrary constant rate, and then in the sense of either (a) first-order…
Double hypergeometric Lévy processes and self-similarity
Andreas E. Kyprianou, Juan Carlos Pardo, Matija Vidmar
Motivated by a recent paper of Budd, where a new family of positive self-similar Markov processes associated to stable processes appears, we introduce a new family of Lévy processe…
The structure of non-linear martingale optimal transport problems
Alexander M. G. Cox, Matija Vidmar
We explore the structure of solutions to a family of non-linear martingale optimal transport (MOT) problems that involve conditional expectations in the objective functional. En ro…
Observing a Lévy process up to a stopping time
Matija Vidmar
It is proved that the law of a possibly killed Lévy process , seen up to and including (resp. up to strictly before) a stopping time, determines already the law of (resp. up…
Excursions of a spectrally negative Lévy process from a two-point set
Matija Vidmar
Let . For a spectrally negative Lévy process with infinite variation paths the resolvent of the process killed on hitting the two-point set is ide…
Arithmetic of (independent) sigma-fields on probability spaces
Matija Vidmar
This note gathers what is known about, and provides some new results concerning the operations of intersection, of ``generated -field'', and of ``complementation'' for (independ…
Exit problems for positive self-similar Markov processes with one-sided jumps
Matija Vidmar
A systematic exposition of scale functions is given for positive self-similar Markov processes (pssMp) with one-sided jumps. The scale functions express as convolution series of th…
A temporal factorization at the maximum for spectrally negative positive self-similar Markov processes
Matija Vidmar
For a spectrally negative positive self-similar Markov process with an a.s. finite overall supremum we provide, in tractable detail, a kind of conditional Wiener-Hopf factorization…
First passage upwards for state dependent-killed spectrally negative Lévy processes
Matija Vidmar
For a spectrally negative Lévy process (snLp) , killed according to a rate that is a function of its position, we analyse the exit probability of the one-sided upwards-passa…
First passage problems for upwards skip-free random walks via the paradigm
Florin Avram, Matija Vidmar
We develop the theory of the and scale functions for right-continuous (upwards skip-free) discrete-time discrete-space random walks, along the lines of the analogue theory…
Independence times for iid sequences, random walks and Lévy processes
Matija Vidmar
For a sequence in discrete time having stationary independent values (respectively, random walk) , those random times of are characterized set-theoretically, for which t…
Another characterization of homogeneous Poisson processes
Matija Vidmar
For a general renewal process (allowing delay, defect and multiple simultaneous arrivals) the independence of the first renewal epochs of the marked processes got from by B…
A couple of remarks on the convergence of -fields on probability spaces
Matija Vidmar
The following modes of convergence of sub--fields on a given probability space have been studied in the literature: weak convergence, strong convergence, convergence with respec…
Ruin under stochastic dependence between premium and claim arrivals
Matija Vidmar
We investigate, focusing on the ruin probability, an adaptation of the Cramer-Lundberg model for the surplus process of an insurance company, in which, conditionally on their inten…
Copulas for maxmin systems
Matija Vidmar, Matjaž Omladič
Under a mild condition we give closed-form expressions for copulas of systems that consist of maxima and of minima of subvectors of a given random vector with continuous margin…