Antonia Foldes - Academia.edu (original) (raw)

Papers by Antonia Foldes

Research paper thumbnail of How Tall Can Be the Excursions of a Random Walk on a Spider

arXiv (Cornell University), Feb 23, 2014

We consider a simple symmetric random walk on a spider, that is a collection of half lines (we ca... more We consider a simple symmetric random walk on a spider, that is a collection of half lines (we call them legs) joined at the origin. Our main question is the following: if the walker makes n steps how high can he go up on all legs. This problem is discussed in two different situations; when the number of legs are increasing, as n goes to infinity and when it is fixed.

Research paper thumbnail of Dedicated to the memory of Marc Yor

We consider a simple symmetric random walk on a spider, that is a collection of half lines (we ca... more We consider a simple symmetric random walk on a spider, that is a collection of half lines (we call them legs) joined at the origin. Our main question is the following: if the walker makes n steps how high can he go up on all legs. This problem is discussed in two different situations; when the number of legs are increasing, as n goes to infinity and when it is fixed.

Research paper thumbnail of Two-Dimensional Anisotropic Random Walks: Fixed Versus Random Column Configurations for Transport Phenomena

Journal of Statistical Physics, 2018

We consider random walks on the square lattice of the plane along the lines of Heyde (1982, 1993)... more We consider random walks on the square lattice of the plane along the lines of Heyde (1982, 1993) and den Hollander (1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics. Twodimensional anisotropic random walks with anisotropic density conditionsá la Heyde (1982, 1983) yield fixed column configurations and nearest-neighbour random walks in a random environment on the square lattice of the plane as in den Hollander (1994) result in random column configurations. In both cases we conclude simultaneous weak Donsker and strong Strassen type invariance principles in terms of appropriately constructed anisotropic Brownian motions on the plane, with selfcontained proofs in both cases. The style of presentation throughout will be that of a semi-expository survey of related results in a historical context.

Research paper thumbnail of Joint asymptotic behavior of local and occupation times of random walk in higher dimension

Studia Scientiarum Mathematicarum Hungarica, 2007

Considering a simple symmetric random walk in dimension d ≧ 3, we study the almost sure joint asy... more Considering a simple symmetric random walk in dimension d ≧ 3, we study the almost sure joint asymptotic behavior of two objects: first the local times of a pair of neighboring points, then the local time of a point and the occupation time of the surface of the unit ball around it.

Research paper thumbnail of Pointwise and Uniform Asymptotics of the Vervaat Error Process

Journal of Theoretical Probability - J THEOR PROBABILITY, 2002

It is well known that, asymptotically, the appropriately normalized uniform Vervaat process, i.e.... more It is well known that, asymptotically, the appropriately normalized uniform Vervaat process, i.e., the integrated uniform Bahadur–Kiefer process properly normalized, behaves like the square of the uniform empirical process. We give a complete description of the strong and weak asymptotic behaviour in sup-norm of this representation of the Vervaat process and, likewise, we also study its pointwise asymptotic behaviour.

Research paper thumbnail of A note on the stability of the local time of a wiener process

Stochastic Processes and their Applications, 1987

It is shown that if g(t) = tl/2(log t)-t(log log t)-p lira A(t)=0 a.s. when p>2 t-I, OO and lim s... more It is shown that if g(t) = tl/2(log t)-t(log log t)-p lira A(t)=0 a.s. when p>2 t-I, OO and lim sup A(t) I> 1 a.s. when p = 1. I-~00 A similar result is proved for random g(t) depending on the maximum of the Wiener process. These results settle a problem posed by Csfrg6 and R6v6sz [7].

Research paper thumbnail of Global Strassen-type theorems for iterated Brownian motions

Stochastic Processes and their Applications, 1995

A class of iterated processes is studied by proving a joint functional limit theorem for a pair o... more A class of iterated processes is studied by proving a joint functional limit theorem for a pair of independent Brownian motions. This Strassen method is applied to prove global (t-~ oc), as well as local (t-, 0), LIL type results for various iterated processes. Similar results are also proved for iterated random walks via invariance.

Research paper thumbnail of On the occupation time of an iterated process having no local time

Stochastic Processes and their Applications, 1997

We study the asymptotic behaviour of the occupation time process J0 14(W~(L~(s)))ds, t >~ 0, wher... more We study the asymptotic behaviour of the occupation time process J0 14(W~(L~(s)))ds, t >~ 0, where t4~ is a standard Wiener process and L2 is a Wiener local time process at zero that is independent from Wi. We prove limit laws, as well as almost sure upper and lower class theorems. Possible extensions of the obtained results are also discussed. ~; 1997 Elsevier Science B.V.

Research paper thumbnail of On the infimum of the local time of a Wiener process

Probability Theory and Related Fields, 1989

Research paper thumbnail of On hardly visited points of the Brownian motion

Probability Theory and Related Fields, 1992

The almost sure behavior of the random measure p(r, q) is investigated.

Research paper thumbnail of On the Number of Cutpoints of the Transient Nearest Neighbor Random Walk on the Line

Journal of Theoretical Probability, 2009

Research paper thumbnail of On the Behavior of Random Walk Around Heavy Points

Journal of Theoretical Probability, 2007

Research paper thumbnail of Random walk on comb-type subsets of Z^2

arXiv: Probability, 2018

We study the path behavior of the simple symmetric walk on some comb-type subsets of Z^2 which ar... more We study the path behavior of the simple symmetric walk on some comb-type subsets of Z^2 which are obtained from Z^2 by removing all horizontal edges belonging to certain sets of values on the y-axis. We obtain some strong approximation results and discuss their consequences.

Research paper thumbnail of Random walk local time approximated by a Wiener sheet combined with an independent Brownian motion

Let xi(k,n)\xi(k,n)xi(k,n) be the local time of a simple symmetric random walk on the line. We give a strong ... more Let xi(k,n)\xi(k,n)xi(k,n) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process xi(k,n)−xi(0,n)\xi(k,n)-\xi(0,n)xi(k,n)−xi(0,n) in terms of a Wiener sheet and an independent Wiener process, time changed by an independent Brownian local time. Some related results and consequences are also established.

Research paper thumbnail of A joint functional law for the Wiener process and principal value

Studia Scientiarum Mathematicarum Hungarica, 2003

We present a joint functional iterated logarithm law for the Wiener process and the principal val... more We present a joint functional iterated logarithm law for the Wiener process and the principal value of its local times.

Research paper thumbnail of Our joint work with Miklós Csörgő

Asymptotic Methods in Stochastics, 2004

Research paper thumbnail of Path properties of Cauchy’s principal values related to local time

Studia Scientiarum Mathematicarum Hungarica, 2001

Sample path properties of the Cauchy principal values of Brownian and random walk local times are... more Sample path properties of the Cauchy principal values of Brownian and random walk local times are studied. We establish LIL type results (without exact constants). Large and small increments are discussed. A strong approximation result between the above two processes is also proved.

Research paper thumbnail of Some Results and Problems for Anisotropic Random Walks on the Plane

Fields Institute Communications, 2015

Research paper thumbnail of Failure-rate estimation in renewal testing

Research paper thumbnail of Random walk on half-plane half-comb structure

We study limiting properties of a random walk on the plane, when we have a square lattice on the ... more We study limiting properties of a random walk on the plane, when we have a square lattice on the upper half-plane and a comb structure on the lower half-plane, i.e., the horizontal lines below the x-axis are removed. We give strong approximations for the components with random time changed Wiener processes. As consequences, limiting distributions and some laws of the iterated logarithm are presented. Finally, a formula is given for the probability that the random walk returns to the origin in 2N steps.

Research paper thumbnail of How Tall Can Be the Excursions of a Random Walk on a Spider

arXiv (Cornell University), Feb 23, 2014

We consider a simple symmetric random walk on a spider, that is a collection of half lines (we ca... more We consider a simple symmetric random walk on a spider, that is a collection of half lines (we call them legs) joined at the origin. Our main question is the following: if the walker makes n steps how high can he go up on all legs. This problem is discussed in two different situations; when the number of legs are increasing, as n goes to infinity and when it is fixed.

Research paper thumbnail of Dedicated to the memory of Marc Yor

We consider a simple symmetric random walk on a spider, that is a collection of half lines (we ca... more We consider a simple symmetric random walk on a spider, that is a collection of half lines (we call them legs) joined at the origin. Our main question is the following: if the walker makes n steps how high can he go up on all legs. This problem is discussed in two different situations; when the number of legs are increasing, as n goes to infinity and when it is fixed.

Research paper thumbnail of Two-Dimensional Anisotropic Random Walks: Fixed Versus Random Column Configurations for Transport Phenomena

Journal of Statistical Physics, 2018

We consider random walks on the square lattice of the plane along the lines of Heyde (1982, 1993)... more We consider random walks on the square lattice of the plane along the lines of Heyde (1982, 1993) and den Hollander (1994), whose studies have in part been inspired by the so-called transport phenomena of statistical physics. Twodimensional anisotropic random walks with anisotropic density conditionsá la Heyde (1982, 1983) yield fixed column configurations and nearest-neighbour random walks in a random environment on the square lattice of the plane as in den Hollander (1994) result in random column configurations. In both cases we conclude simultaneous weak Donsker and strong Strassen type invariance principles in terms of appropriately constructed anisotropic Brownian motions on the plane, with selfcontained proofs in both cases. The style of presentation throughout will be that of a semi-expository survey of related results in a historical context.

Research paper thumbnail of Joint asymptotic behavior of local and occupation times of random walk in higher dimension

Studia Scientiarum Mathematicarum Hungarica, 2007

Considering a simple symmetric random walk in dimension d ≧ 3, we study the almost sure joint asy... more Considering a simple symmetric random walk in dimension d ≧ 3, we study the almost sure joint asymptotic behavior of two objects: first the local times of a pair of neighboring points, then the local time of a point and the occupation time of the surface of the unit ball around it.

Research paper thumbnail of Pointwise and Uniform Asymptotics of the Vervaat Error Process

Journal of Theoretical Probability - J THEOR PROBABILITY, 2002

It is well known that, asymptotically, the appropriately normalized uniform Vervaat process, i.e.... more It is well known that, asymptotically, the appropriately normalized uniform Vervaat process, i.e., the integrated uniform Bahadur–Kiefer process properly normalized, behaves like the square of the uniform empirical process. We give a complete description of the strong and weak asymptotic behaviour in sup-norm of this representation of the Vervaat process and, likewise, we also study its pointwise asymptotic behaviour.

Research paper thumbnail of A note on the stability of the local time of a wiener process

Stochastic Processes and their Applications, 1987

It is shown that if g(t) = tl/2(log t)-t(log log t)-p lira A(t)=0 a.s. when p>2 t-I, OO and lim s... more It is shown that if g(t) = tl/2(log t)-t(log log t)-p lira A(t)=0 a.s. when p>2 t-I, OO and lim sup A(t) I> 1 a.s. when p = 1. I-~00 A similar result is proved for random g(t) depending on the maximum of the Wiener process. These results settle a problem posed by Csfrg6 and R6v6sz [7].

Research paper thumbnail of Global Strassen-type theorems for iterated Brownian motions

Stochastic Processes and their Applications, 1995

A class of iterated processes is studied by proving a joint functional limit theorem for a pair o... more A class of iterated processes is studied by proving a joint functional limit theorem for a pair of independent Brownian motions. This Strassen method is applied to prove global (t-~ oc), as well as local (t-, 0), LIL type results for various iterated processes. Similar results are also proved for iterated random walks via invariance.

Research paper thumbnail of On the occupation time of an iterated process having no local time

Stochastic Processes and their Applications, 1997

We study the asymptotic behaviour of the occupation time process J0 14(W~(L~(s)))ds, t >~ 0, wher... more We study the asymptotic behaviour of the occupation time process J0 14(W~(L~(s)))ds, t >~ 0, where t4~ is a standard Wiener process and L2 is a Wiener local time process at zero that is independent from Wi. We prove limit laws, as well as almost sure upper and lower class theorems. Possible extensions of the obtained results are also discussed. ~; 1997 Elsevier Science B.V.

Research paper thumbnail of On the infimum of the local time of a Wiener process

Probability Theory and Related Fields, 1989

Research paper thumbnail of On hardly visited points of the Brownian motion

Probability Theory and Related Fields, 1992

The almost sure behavior of the random measure p(r, q) is investigated.

Research paper thumbnail of On the Number of Cutpoints of the Transient Nearest Neighbor Random Walk on the Line

Journal of Theoretical Probability, 2009

Research paper thumbnail of On the Behavior of Random Walk Around Heavy Points

Journal of Theoretical Probability, 2007

Research paper thumbnail of Random walk on comb-type subsets of Z^2

arXiv: Probability, 2018

We study the path behavior of the simple symmetric walk on some comb-type subsets of Z^2 which ar... more We study the path behavior of the simple symmetric walk on some comb-type subsets of Z^2 which are obtained from Z^2 by removing all horizontal edges belonging to certain sets of values on the y-axis. We obtain some strong approximation results and discuss their consequences.

Research paper thumbnail of Random walk local time approximated by a Wiener sheet combined with an independent Brownian motion

Let xi(k,n)\xi(k,n)xi(k,n) be the local time of a simple symmetric random walk on the line. We give a strong ... more Let xi(k,n)\xi(k,n)xi(k,n) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process xi(k,n)−xi(0,n)\xi(k,n)-\xi(0,n)xi(k,n)−xi(0,n) in terms of a Wiener sheet and an independent Wiener process, time changed by an independent Brownian local time. Some related results and consequences are also established.

Research paper thumbnail of A joint functional law for the Wiener process and principal value

Studia Scientiarum Mathematicarum Hungarica, 2003

We present a joint functional iterated logarithm law for the Wiener process and the principal val... more We present a joint functional iterated logarithm law for the Wiener process and the principal value of its local times.

Research paper thumbnail of Our joint work with Miklós Csörgő

Asymptotic Methods in Stochastics, 2004

Research paper thumbnail of Path properties of Cauchy’s principal values related to local time

Studia Scientiarum Mathematicarum Hungarica, 2001

Sample path properties of the Cauchy principal values of Brownian and random walk local times are... more Sample path properties of the Cauchy principal values of Brownian and random walk local times are studied. We establish LIL type results (without exact constants). Large and small increments are discussed. A strong approximation result between the above two processes is also proved.

Research paper thumbnail of Some Results and Problems for Anisotropic Random Walks on the Plane

Fields Institute Communications, 2015

Research paper thumbnail of Failure-rate estimation in renewal testing

Research paper thumbnail of Random walk on half-plane half-comb structure

We study limiting properties of a random walk on the plane, when we have a square lattice on the ... more We study limiting properties of a random walk on the plane, when we have a square lattice on the upper half-plane and a comb structure on the lower half-plane, i.e., the horizontal lines below the x-axis are removed. We give strong approximations for the components with random time changed Wiener processes. As consequences, limiting distributions and some laws of the iterated logarithm are presented. Finally, a formula is given for the probability that the random walk returns to the origin in 2N steps.