17 citations · 74 across the 18 of their papers we have counts for
6 papers · 2 filters
Strong approximation of fractional Brownian motion by moving averages of simple random walks
Tamas Szabados
The fractional Brownian motion is a generalization of ordinary Brownian motion, used particularly when long-range dependence is required. Its explicit introduction is due to B.B. M…
An elementary approach to Brownian local time based on simple, symmetric random walks
Tamas Szabados, Balazs Szekely
In this paper we define Brownian local time as the almost sure limit of the local times of a nested sequence of simple, symmetric random walks. The limit is jointly continuous in $…
An exponential functional of random walks
Tamas Szabados, Balazs Szekely
The aim of this paper is to investigate discrete approximations of the exponential functional $\int_0^{\infty} \exp(B(t) - νt) \di t$ of Brownian motion (which plays an important r…
An elementary introduction to the Wiener process and stochastic integrals
Tamas Szabados
An elementary construction of the Wiener process is discussed, based on a proper sequence of simple symmetric random walks that uniformly converge on bounded intervals, with probab…
Strong approximation of continuous local martingales by simple random walks
Balazs Szekely, Tamas Szabados
The aim of this paper is to represent any continuous local martingale as an almost sure limit of a nested sequence of simple, symmetric random walks, time changed by a discrete qua…
Self-intersection local time of planar Brownian motion based on a strong approximation by random walks
Tamás Szabados
The main purpose of this work is to define planar self-intersection local time by an alternative approach which is based on an almost sure pathwise approximation of planar Brownian…