Vigirdas Mackevičius
Vilnius University
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Publication
Featured researches published by Vigirdas Mackevičius.
Stochastic Processes and their Applications | 1998
François Coquet; Vigirdas Mackevičius; Jean Mémin
We consider a cadlag process the filtration generated by Y and generated by step processes Yn defined from Y by discretization in time. We study the stability in (with Skorokhod topology) of -martingales and of -solutions of related backward equations, when Yn-->Y. We get this stability (in law) when Y is Markov and (in probability) under stronger assumptions on the coefficients of equations.
Mathematics and Computers in Simulation | 2001
Vigirdas Mackevičius; Jurgis Navikas
A ‘standard’ second order weak Runge–Kutta method for a stochastic differential equation can be applied only in the case where the equation is understood in the Stratonovich sense. To adapt Runge–Kutta type methods for Ito equations, we propose to use a rather simple additional derivative-free term.
Lithuanian Mathematical Journal | 2000
François Coquet; Jean Mémin; Vigirdas Mackevičius
We study some properties of the weak convergence of filtrations, in particular, its behavior under elementary set operations. We also derive relations between the convergence of filtrations generated by point processes with a single jump and the convergence of their compensators or distributions of their jump moments. Finally, we apply a lemma on the intersection of σ-algebras to filtrations generated by different discretizations of a single process.
Statistics & Probability Letters | 2003
Bronius Grigelionis; Vigirdas Mackevičius
It is well known that the stochastic exponential , of a continuous local martingale M has expectation EZt=1 and, thus, is a martingale if (Novikovs condition). We show that, for p>1, EZtp t} 0. As a consequence, we get that the moments of the stochastic exponential of a stochastic integral with respect to a Brownian motion are all finite, provided the integrand is a Brownian functional of linear growth.
Mathematics and Computers in Simulation | 2000
Vigirdas Mackevičius
The phenomenon of ‘synchronization’ of physical diffusion is widely discussed in the physical literature. In this paper, we give a simple rigorous proof of the synchronization for a one-dimensional diffusion including the one-dimensional counterpart of a physical diffusion described by a degenerate two-dimensional stochastic differential equation.
Mathematics and Computers in Simulation | 2015
A. Lenksas; Vigirdas Mackevičius
We construct a first-order weak split-step approximation for the solution of the Heston model that uses, at each step, generation of two discrete two-valued random variables. The Heston equation system is split into the deterministic part, solvable explicitly, and the stochastic part that is approximated by discrete random variables. The approximation is illustrated by several simulation examples, including applications to option pricing.
Mathematics and Computers in Simulation | 1997
Vigirdas Mackevičius
Let Xt, t ∈ [0,T], be the solution of a stochastic differential equation, and let Xth, t ∈ [0,T], be the Euler approximation with the step h = Tn. It is known that, for a wide class of functions f, the error Ef(XTh) − Ef(XT) is O(h) or, more exactly, C · h + O(h2). We propose an extension of these results to a class of functionals f depending on the trajectories of the solution on the whole time interval [0,T]. The functionals are defined on an appropriate semi-martingale space.
Lithuanian Mathematical Journal | 1994
Vigirdas Mackevičius
Lithuanian Mathematical Journal | 2015
Vigirdas Mackevičius
Stochastic Processes and their Applications | 1999
François Coquet; Vigirdas Mackevičius; Jean Mémin