38 citations · 70 across the 12 of their papers we have counts for
9 papers · 1 filter
Example of a Dirichlet process whose zero energy part has finite p-variation
Vilmos Prokaj, László Bondici
Let be a fractional Brownian motion on with Hurst parameter , be its pathwise antiderivative with , and let be a standard Brownian mot…
On the lack of semimartingale property
Vilmos Prokaj, László Bondici
In this work we extend the characterization of semimartingale functions in Cinlar et al. (1980) to the non-Markovian setting. We prove that if a function of a semimartingale remain…
Local martingales in discrete time
Vilmos Prokaj, Johannes Ruf
For any discrete-time --local martingale there exists a probability measure such that is a --martingale. A new proof for this result is provided. The core…
Stochastic Integral Equations for Walsh Semimartingales
Tomoyuki Ichiba, Ioannis Karatzas, Vilmos Prokaj +1
We construct planar semimartingales that include the Walsh Brownian motion as a special case, and derive Harrison-Shepp-type equations and a change-of-variable formula in the spiri…
On the exactness of the Levy-transformation
Vilmos Prokaj
In a recent paper we gave a sufficient condition for the strong mixing property of the Levy-transformation. In this note we show that it actually implies a much stronger property,…
Some sufficient conditions for the ergodicity of the Lévy transformation
Vilmos Prokaj
We propose a possible way of attacking the question posed originally by Daniel Revuz and Marc Yor in their book published in 1991. They were asking whether the Lévy transformation…
Diffusions with rank-based characteristics and values in the nonnegative quadrant
Tomoyuki Ichiba, Ioannis Karatzas, Vilmos Prokaj
We construct diffusions with values in the nonnegative orthant, normal reflection along each of the axes, and two pairs of local drift/variance characteristics assigned according t…
Planar Diffusions with Rank-Based Characteristics: Transition Probabilities, Time Reversal, Maximality and Perturbed Tanaka equations
E. Robert Fernholz, Tomoyuki Ichiba, Ioannis Karatzas +1
We construct a planar diffusion process whose infinitesimal generator depends only on the order of the components of the process. Speaking informally and a bit imprecisely for the…
The solution of the perturbed Tanaka-equation is pathwise unique
Vilmos Prokaj
The Tanaka equation is an example of a stochastic differential equation (SDE) without strong solution. Hence pathwise uniqueness does not ho…