17 citations · 74 across the 18 of their papers we have counts for
19 papers
Factorization of a spectral density with smooth eigenvalues of a multidimensional stationary time series
Tamás Szabados
The aim of this paper to give a multidimensional version of the classical one-dimensional case of smooth spectral density. A smooth spectral density gives an explicit method to fac…
Regular multidimensional stationary time series
Tamás Szabados
The aim of this paper is to give a simpler, more usable sufficient condition to the regularity of generic weakly stationary time series. Also, this condition is used to show how re…
Pathwise approximation of Feynman path integrals using simple random walks
Tamás Szabados
The aim of the presented research is to give a rigorous mathematical approach to Feynman path integrals based on strong (pathwise) approximations based on simple random walks.
A simple wide range approximation of symmetric binomial distributions
Tamás Szabados
The paper gives a wide range, uniform, local approximation of symmetric binomial distribution. The result clearly shows how one has to modify the the classical de Moivre--Laplace n…
The fallacy of tumor immunology: Evolutionary pressures, viruses as nature's genetic engineering tools and T cell surveillance emergence for purging nascent selfish cells
Tibor Bakacs, Katalin Kristof, Jitendra Mehrishi +4
The US and Hungarian statistical records of the years 1900 and 1896, respectively, before the dramatic medical advances, show 32% and 27% deaths attributable to infections, whereas…
MiStImm: a simulation tool to compare classical nonsef-centered immune models with a novel self-centered model
Tamás Szabados, Csaba Kerepesi, Tibor Bakács
Our main purpose is to compare classical nonself-centered, two-signal theoretical models of the adaptive immune system with a novel, self-centered, one-signal model developed by ou…
A stochastic model of B cell affinity maturation and a network model of immune memory
Tamás Szabados, Gábor Tusnády, László Varga +1
Many events in the vertebrate immune system are influenced by some element of chance. The objective of the present work is to describe affinity maturation of B lymphocytes (in whic…
Strong approximation of Black--Scholes theory based on simple random walks
Zsolt Nika, Tamás Szabados
A basic model in financial mathematics was introduced by Black, Scholes and Merton in 1973 (BSM model). A classical discrete approximation in distribution is the binomial model giv…
Kolmogorov complexity and strong approximation of Brownian motion
Bjørn Kjos-Hanssen, Tamás Szabados
Brownian motion and scaled and interpolated simple random walk can be jointly embedded in a probability space in such a way that almost surely the -step walk is within a uniform…
An approximation of Itô diffusions based on simple random walks
John van der Hoek, Tamas Szabados
The aim of this paper is to develop a sequence of discrete approximations to a one-dimensional Itô diffusion that almost surely converges to a weak solution of the given stochastic…
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 $…
Moments of an exponential functional of random walks and permutations with given descent sets
Tamas Szabados, Balazs Szekely
The exponential functional of simple, symmetric random walks with negative drift is an infinite polynomial of independent and identicall…
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…
A new homeostatic model of the T cell system
Tamas Szabados, Tibor Bakacs
Our main tenet argues that the primary role of positive thymic selection and the resulting T cell population is the maintenance of a homeostatic equilibrium with self MHC-self pept…
Stochastic integration based on simple, symmetric random walks
Tamás Szabados, Balázs Székely
A new approach to stochastic integration is described, which is based on an a.s. pathwise approximation of the integrator by simple, symmetric random walks. Hopefully, this method…