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Papers by Joanna Mitro

For Additive Functionals in Weak Duality

General theory of markov processes

Stochastics and Stochastics Reports, May 1, 1991

General theory of markov processes, by Michael Sharpe, University of California at San Diego. Aca... more General theory of markov processes, by Michael Sharpe, University of California at San Diego. Academic Press, New York (1988), 419 pp. $49.50. ISBN 0-12-639060-6.

For Additive Functionals in Weak Duality

General theory of markov processes

Stochastics and Stochastic Reports, 1991

General theory of markov processes, by Michael Sharpe, University of California at San Diego. Aca... more General theory of markov processes, by Michael Sharpe, University of California at San Diego. Academic Press, New York (1988), 419 pp. $49.50. ISBN 0-12-639060-6.

Bulletin of the American Mathematical Society, 1991

The type problem for random walks on trees

J Theor Probability, 1991

We consider the question of whether the simple random walk (SRW) on an infinite tree is transient... more We consider the question of whether the simple random walk (SRW) on an infinite tree is transient or recurrent. For random M-trees (all vertices of distance n from the root of the tree have degree d,, where {d,} are independent random variables), we prove that the SRW is as transient if ...

Book Review: Probabilit�s et potentiel

Bull Amer Math Soc, 1991

A discontinuous time change for natural additive functionals which preserves duality

Probability Theory and Related Fields, 1986

... Joanna B. Mitro* Department of Mathematical Sciences, University of Cincinnati, Cincinnati, O... more ... Joanna B. Mitro* Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, USA ... are right continuous, with left limits in E on (0, ~). Both processes become coordinate processes on this space, and are distin-guished by the measures px and fix. ...

Applications of Revuz and Palm Type Measures for Additive Functionals in Weak Duality

Seminar on Stochastic Processes, 1982, 1983

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1984

In 1975 Maisonneuve [13] introduced the "exit system", a kernel/additive functional pair (*P,B) a... more In 1975 Maisonneuve [13] introduced the "exit system", a kernel/additive functional pair (*P,B) associated to a homogeneous random set, as a general tool for studying the excursions of Markov processes (a similar idea had been suggested by Dynkin [5] in 1971). In [6-I Getoor used the exit system to analyze specific excursions, and recently exit systems were used by Getoor and Sharpe [7, 9-1 to study excursions under duality hypotheses. The purpose of this paper is to explore the relationship between "dual" exit systems (*P,B) and (*P, B) of a pair of dual Markov processes, by means of an auxiliary "twosided" Markov process with random birth and death in which the original dual processes may be simultaneously realized. The object of our study is to contribute to the theory of excursions of dual processes, using the auxiliary process as a convenient and natural tool. Section 1 introduces the two-sided processes we will use throughout the paper, and establishes our notation. Sections 2 and 3 concern exit systems and excursions of the auxiliary process. We introduce and exploit the notion of "co-exit system", which comes from the dual exit system. The presentation of this part of the paper was influenced by Maisonneuve's recent work on regenerative sets on the real line [12] and benefited greatly from his comments. In Sect. 4 we look again at the original dual processes. Here we generalize the result of [9] on reversing excursions from a point, eliminating the hypothesis of dual densities. This section also contains a formula (first discovered by Kaspi [11]) which expresses a duality relationship between the dual exit systems. See Sect. 4 for the precise statements.

A Time Reversal Study of Exit/Entrance Processes

Seminar on Stochastic Processes, 1984, 1986

Discontinuous Time Changes and Duality for Markov Processes

Seminar on Stochastic Processes, 1985, 1986

Stochastic Processes and their Applications, 1986

The "time change" of a Markov process via the inverse of a discontinuous additive functional A, c... more The "time change" of a Markov process via the inverse of a discontinuous additive functional A, can be accomplished in two steps. First, perform a time change via the inverse of the strictly increasing discontinuous additive functional obtained by replacing the continuous part of A, by t. The second step is an ordinary time change via the inverse of a continuous additive functional. Decomposing the time change in this way is useful in studying the time changed process.

Stochastic Processes and their Applications, 1988

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1979

Dual Markov processes: Construction of a useful auxiliary process

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1979

... Joanna B. Mitro Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana... more ... Joanna B. Mitro Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA ... Begin by constructing, for each real t, a measure Qt carried by ~t={QOe@: ~(t)~E}. Fix t, and define ~(- 0% t) to be the space of paths ~ from (- 0% t) into E ...

Modeling and Performance of a Mesh Network with Dynamically Appearing and Disappearing Femtocells as Additional Internet Gateways

IEEE Transactions on Parallel and Distributed Systems, 2000

ABSTRACT The number of hops from Mesh Routers (MRs) to an Internet gateway (IGW) plays an importa... more ABSTRACT The number of hops from Mesh Routers (MRs) to an Internet gateway (IGW) plays an important role in determining the performance of a wireless mesh network (WMN). A recent patent has introduced a mechanism of using an existing femtocell (FC) as an additional potential IGW so that the performance of a WMN could be enhanced. Such an integration of WMN with FCs enables an increase in WMN's overall capacity. But, due to FCs' unpredictable operating times and uninformed disconnections, MRs require reliable and efficient schedule for switching between available FCs which has not been analyzed in the patent. The switching can be done in a push based preemptive or a pull based non-preemptive manner. In this paper, we formulate both these switching schemes for a WMN-FC integrated network as approximate statistical models based on a Markovian process. We also determine a switching schedule of FCs for each of MR based on reliable uncapacitated facility location (RUFL) problem. We extend an existing RUFL problem to incorporate dynamic operating nature of multiple FCs which display dynamic available/unavailable patterns for additional potential IGWs. Extensive simulations are carried out to validate our proposed statistical models and establish the performance of these switching schemes.

Symmetries and Functions of Markov Processes

The Annals of Probability, 1990

... 18, No. 2, 655-668 SYMMETRIES AND FUNCTIONS OF MARKOV PROCESSES BY JOSEPH GLOVER 1 AND JOANNA... more ... 18, No. 2, 655-668 SYMMETRIES AND FUNCTIONS OF MARKOV PROCESSES BY JOSEPH GLOVER 1 AND JOANNA MITRO2 University of Florida and University of Cincinnati ... Fix a subgroup H of G, and use H to define F and (F as follows. ...

Stochastic processes and their applications, 1984

The process (X. I), where X is a Markov process and 1 its local time at a regular point h. is rev... more The process (X. I), where X is a Markov process and 1 its local time at a regular point h. is reversed from the time I first exceeds the level 1, and the resulting process is identified under duality hypotheses. The approach exploits recent results in the theory of excursions of dual processes.

For Additive Functionals in Weak Duality

General theory of markov processes

Stochastics and Stochastics Reports, May 1, 1991

General theory of markov processes, by Michael Sharpe, University of California at San Diego. Aca... more General theory of markov processes, by Michael Sharpe, University of California at San Diego. Academic Press, New York (1988), 419 pp. $49.50. ISBN 0-12-639060-6.

For Additive Functionals in Weak Duality

General theory of markov processes

Stochastics and Stochastic Reports, 1991

General theory of markov processes, by Michael Sharpe, University of California at San Diego. Aca... more General theory of markov processes, by Michael Sharpe, University of California at San Diego. Academic Press, New York (1988), 419 pp. $49.50. ISBN 0-12-639060-6.

Bulletin of the American Mathematical Society, 1991

The type problem for random walks on trees

J Theor Probability, 1991

We consider the question of whether the simple random walk (SRW) on an infinite tree is transient... more We consider the question of whether the simple random walk (SRW) on an infinite tree is transient or recurrent. For random M-trees (all vertices of distance n from the root of the tree have degree d,, where {d,} are independent random variables), we prove that the SRW is as transient if ...

Book Review: Probabilit�s et potentiel

Bull Amer Math Soc, 1991

A discontinuous time change for natural additive functionals which preserves duality

Probability Theory and Related Fields, 1986

... Joanna B. Mitro* Department of Mathematical Sciences, University of Cincinnati, Cincinnati, O... more ... Joanna B. Mitro* Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, USA ... are right continuous, with left limits in E on (0, ~). Both processes become coordinate processes on this space, and are distin-guished by the measures px and fix. ...

Applications of Revuz and Palm Type Measures for Additive Functionals in Weak Duality

Seminar on Stochastic Processes, 1982, 1983

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1984

In 1975 Maisonneuve [13] introduced the "exit system", a kernel/additive functional pair (*P,B) a... more In 1975 Maisonneuve [13] introduced the "exit system", a kernel/additive functional pair (*P,B) associated to a homogeneous random set, as a general tool for studying the excursions of Markov processes (a similar idea had been suggested by Dynkin [5] in 1971). In [6-I Getoor used the exit system to analyze specific excursions, and recently exit systems were used by Getoor and Sharpe [7, 9-1 to study excursions under duality hypotheses. The purpose of this paper is to explore the relationship between "dual" exit systems (*P,B) and (*P, B) of a pair of dual Markov processes, by means of an auxiliary "twosided" Markov process with random birth and death in which the original dual processes may be simultaneously realized. The object of our study is to contribute to the theory of excursions of dual processes, using the auxiliary process as a convenient and natural tool. Section 1 introduces the two-sided processes we will use throughout the paper, and establishes our notation. Sections 2 and 3 concern exit systems and excursions of the auxiliary process. We introduce and exploit the notion of "co-exit system", which comes from the dual exit system. The presentation of this part of the paper was influenced by Maisonneuve's recent work on regenerative sets on the real line [12] and benefited greatly from his comments. In Sect. 4 we look again at the original dual processes. Here we generalize the result of [9] on reversing excursions from a point, eliminating the hypothesis of dual densities. This section also contains a formula (first discovered by Kaspi [11]) which expresses a duality relationship between the dual exit systems. See Sect. 4 for the precise statements.

A Time Reversal Study of Exit/Entrance Processes

Seminar on Stochastic Processes, 1984, 1986

Discontinuous Time Changes and Duality for Markov Processes

Seminar on Stochastic Processes, 1985, 1986

Stochastic Processes and their Applications, 1986

The "time change" of a Markov process via the inverse of a discontinuous additive functional A, c... more The "time change" of a Markov process via the inverse of a discontinuous additive functional A, can be accomplished in two steps. First, perform a time change via the inverse of the strictly increasing discontinuous additive functional obtained by replacing the continuous part of A, by t. The second step is an ordinary time change via the inverse of a continuous additive functional. Decomposing the time change in this way is useful in studying the time changed process.

Stochastic Processes and their Applications, 1988

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1979

Dual Markov processes: Construction of a useful auxiliary process

Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, 1979

... Joanna B. Mitro Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana... more ... Joanna B. Mitro Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA ... Begin by constructing, for each real t, a measure Qt carried by ~t={QOe@: ~(t)~E}. Fix t, and define ~(- 0% t) to be the space of paths ~ from (- 0% t) into E ...

Modeling and Performance of a Mesh Network with Dynamically Appearing and Disappearing Femtocells as Additional Internet Gateways

IEEE Transactions on Parallel and Distributed Systems, 2000

ABSTRACT The number of hops from Mesh Routers (MRs) to an Internet gateway (IGW) plays an importa... more ABSTRACT The number of hops from Mesh Routers (MRs) to an Internet gateway (IGW) plays an important role in determining the performance of a wireless mesh network (WMN). A recent patent has introduced a mechanism of using an existing femtocell (FC) as an additional potential IGW so that the performance of a WMN could be enhanced. Such an integration of WMN with FCs enables an increase in WMN's overall capacity. But, due to FCs' unpredictable operating times and uninformed disconnections, MRs require reliable and efficient schedule for switching between available FCs which has not been analyzed in the patent. The switching can be done in a push based preemptive or a pull based non-preemptive manner. In this paper, we formulate both these switching schemes for a WMN-FC integrated network as approximate statistical models based on a Markovian process. We also determine a switching schedule of FCs for each of MR based on reliable uncapacitated facility location (RUFL) problem. We extend an existing RUFL problem to incorporate dynamic operating nature of multiple FCs which display dynamic available/unavailable patterns for additional potential IGWs. Extensive simulations are carried out to validate our proposed statistical models and establish the performance of these switching schemes.

Symmetries and Functions of Markov Processes

The Annals of Probability, 1990

... 18, No. 2, 655-668 SYMMETRIES AND FUNCTIONS OF MARKOV PROCESSES BY JOSEPH GLOVER 1 AND JOANNA... more ... 18, No. 2, 655-668 SYMMETRIES AND FUNCTIONS OF MARKOV PROCESSES BY JOSEPH GLOVER 1 AND JOANNA MITRO2 University of Florida and University of Cincinnati ... Fix a subgroup H of G, and use H to define F and (F as follows. ...

Stochastic processes and their applications, 1984

The process (X. I), where X is a Markov process and 1 its local time at a regular point h. is rev... more The process (X. I), where X is a Markov process and 1 its local time at a regular point h. is reversed from the time I first exceeds the level 1, and the resulting process is identified under duality hypotheses. The approach exploits recent results in the theory of excursions of dual processes.