Dr. Dshalalow's research interests include real and stochastic analysis, random measures, mathematical models in cell-molecular biology, in particule, of cancer growth, stochastic finance, antagonistic games, and queueing theory.
M.S. Berlin Technical University 1979
Dr. Sci. Berlin Technical University 1983
The following mathematicians and scientists were among Dr. Dshalalow's “academic ancestors.”
Johann Radon, Rudolf Lipschitz, Gustav Dirichlet, Ferdinand Frobenius, Karl Weierstraß, Friedrich Bessel, Carl Friedrich Gauß, Simeon Poisson, Joseph Lagrange, Leonhard Euler, Jacob Bernoulli, Gottfried von Leibniz, and Nicolaus Copernicus.
See Dr. Dshalalow's academic genealogy
Dr. Dshalalow is currently the editor-in-chief of Mathematics and Statistics. He had also been the editor-in-chief of the Journal of Applied Mathematics and Stochastic Analysis. He is a regional editor of the Engineering Simulation. He is also an associate editor of seven other international journals, including Journal of Inequalities and Applications and Intern. Journal of Mathematics and Mathematical Sciences, Abstract and Applied Analysis.
Dr. Dshalalow wrote a graduate level textbook Foundations of Abstract Analysis published by Springer New York, 2013, Real Analysis, a graduate level textbook, by Chapman & Hall, 2001, and two books, Advances in Queuing and Frontiers in Queuing by CRC Press, that appeared in 1995 and 1997, respectively.
From 1993 to 2019, Dr. Dshalalow supervised 21 doctoral students in the areas of stochastic analysis, random measures, stochastic games, mathematical finance, and queueing theory, see Math Genealogy Project at http://genealogy.math.ndsu.nodak.edu/id.php?id=19878.
Spring 2017, Stochastic Analysis of Financial Markets, MTH 5434/ORP 5025, Probability/Statistics, MTH 2401, Applied Discrete Mathematics, MTH 5051.
Spring 2018, MTH 3101, Complex Variables, MTH 2401, Probability and Statistics, MTH 5051, Applied Discrete Mathematics.
Fall 2018, Probability/Statistics, MTH 2401, Stochastic Modeling MTH 4202, Math Stat 1 MTH 5411.
Spring 2019, MTH 5420 Theory of Stochastic Processes, MTH 3663 Methods for Biomath.
Fall 2020, MTH 5111/MTH 4111 Real Variables I/Honors Analysis, MTH 5051 Applied Discrete Mathematics
Fall 2021 MTH 2401 Probability/Stat, MTH 5051 Applied Discrete Mathematics
GRADUATE COURSES: Stochastic Processes, Real Variables, Applied Discrete Mathematics, Stochastic Analysis of Financial Markets, Queueing Theory, Stochastic Signals, Statistics I and II, Stochastic Models, Complex Variables, Introductory Analysis.
UNDERGRADUATE COURSES: Biostochastics, Topology, Probability and Statistics, Linear Algebra, Complex Variables, Boundary Value Problems, Differential Equations, Calculus III, Methods for Biomath, Stochastic Modeling.
Random walk analysis in a reliability system under constant degradation and random shocks, accepted for publication in Axioms.
Current trends in random walks on random lattices (joointly with Ryan White), Mathematics, 9 (2021), 1-38.
Time sensitive analysis of antagonistic stochastic games with applications to finance and queueing (jointly with Kizza Nandyose and Ryan White), Mathematics and Statistics, 9:4 (2021), 481-500.
Characterizations of random walks on random lattices and their ramifications (jointly with Ryan White), Stochastic Analysis & Appl's, 38:2 (2020), 307-342.
Characterization of generalized Poisson measures on topological spaces (jointly with Ali Al-Obaidi), Stoch Analysis and Appl's, (2021), 525-548.
Fluctuation analysis in parallel queues with hysteretic control (jointly with Ahmed Merie and Ryan White), Methodology and Computing in Applied Probability, Springer NY, 22:1 (2020), 295-307.
On intensities of perturbed random measures on Hausdorff spaces (jointly with Ali Al-Obaidi), Stochastic Analysis and Applications, 36:6 (2018), 932-959.
Real Time Analysis of Signed Marked Random Measures with Applications to Finance and Insurance (jointly with Kizza Nandyose), Nonlinear Dynamics and System Theory, 19:1 (2019), 36-54.
Fluctuation analysis in queues with several operational modes and priority customers (jointly with Ahmed Merie), TOP, Springer, NY, 26 (2018), 309-333.
Continuous time interpolation of monotone marked random measures with applications (jointly with Kizza Nandyose), Neural, Parallel, and Scientific Computations, 26:2 (2018), 119-141.
Discrete versus continuous operational calculus in antagonistic stochastic games (jointly with Kenneth Iwezulu), São Paulo Journal of Math. Sci., Springer, NY, 11 (2017), 471-489.
Time sensitive analysis of independent and stationary increments processes (jointly with Ryan T. White), Journal of Mathematical Analysis and Applications 443 (2016), 817-833.
Discrete operational calculus in delayed stochastic games (jointly with Kenneth Iwezulu and Ryan White), Neural, Parallel, and Scientific Computations 24 (2016), 55-64.
On tractable functionals in antagonistic games with a constant initial condition (jointly with Weijun Huang, Hao-Jan Ke, and Ailada Treerattrakoon), Nonlinear Dynamics and System Theory, 16:1 (2016) 1-14.
On strategic defense in stochastic networks (jointly with Ryan White), Stochastic Analysis and Applications, 32 (2014), 365-396.
On reliability of stochastic networks (jointly with Ryan White), Neural, Parallel, and Scientific Computations, 21 (2013) 141-160.
On one-sided stochastic games and their applications to finance (jointly with Randy Robinson), Stochastic Models, 28 (2012), 1-14.
On unbiased and consistent estimator for mutation rates, (jointly with Niccum, B.A., Poteau, R., Hamman, G.E., Varada, J.C. and Sinden, R.R.) Journal of Theoretical Biology, 300 (2012), 360-367.
Time sensitive functionals in classes of queues with sequential maintenance (jointly with N. Al-Matar), Stochastic Models: In the Special Issue Dedicated to Marcel Neuts, 27 (2011), 687-704.
Anatolii Andreevich Martynuyk (jointly with P. Borne, Freedman, H., C. Gaishun, C. Izobov, Cruz-Hernandes, Z., Samoilenko, A., Stavrulakis, I., Sun Zhen qi), Journal of Differential Equations, 47:3 (2011), 305-306
On fluctuations of a nonmonotone marked point process under a time constraint (jointly with Randy Robinson), Neural, Parallel, and Scientific Computations, 20 (2012), 249-262.
Fluctuation analysis in a queue with (L-N)-policy and secondary maintenance. Continuous time parameter process and numerics (jointly with M. Alzahrani), Engineering Simulation, 33:5 (2011), 19-42.
Sequential antagonistic games with initial phase (with W. Huang), in FUNCTIONAL EQUATIONS AND DIFFERENCE INEQUALITIES AND ULAM STABILITY NOTIONS , Dedicated to Stanislaw ULAM, on his 100-th birthday anniversary, Chapter 2, (2010) 15-36, Nova Sci. Publ.
Operational calculus in noncooperative stochastic games (with A. Treerattrakoon), Nonlinear Dynamics and System Theory, 10:1 (2010), 39-54.
Multilayers in a Modulated Stochastic Game (with Hao-Jan Ke), Journ. of Math. Analysis and Applications, 353 (2009), 553-565.
Multiphase fluctuation analysis in a queue with an enhanced maintenance. Continuous time parameter process (with A. Alghamdi), Nonlinear Studies, 17:3 (2010), 199-215.
Tandem antagonistic games (with W. Huang), Nonlinear Analysis, Series A, Theory and Methods, 71 (2009), 259-270.
Maintenance in single-server queues. A game-theoretic approach (with N. Al-Matar), Mathematical Problems in Engineering, Vol. 2009, 1-23.
Random walk analysis in antagonistic stochastic games, Stoch. Analysis and Applications 26 (2008), 738-783.
Set-theoretic inequalities in stochastic noncooperative games with coalition (with A. Treerattrakoon), Journal of Inequalities and Applications, 2008.
On multivariate antagonistic marked point processes, Math. and Comp. Modeling, 49 (2009) 432-452.
Characterization of modulated Cox measures on topological spaces, in special volume dedicated to tricentennial of L. Euler, Int Journ Appl Math Stat, 11:7, 2007.
A stochastic games with a two-phase conflict (with W. Huang), in Jubilee Volume: Legacy of the Legend, Professor V. Lakshmikantham, Cambridge Scientific Publishers, 2009.
On Dual hybrid queueing systems (with L. Abolnikov and A. Treerattrakoon), Nonlin Analysis; Hybrid Systems, 2:1 (2008), 96-109
Random Walk Analysis of Parallel Queueing Stations, Math. and Comp. Modeling (with L. Abolnikov and R. Agarwal), 47, 2008, 452-468
On exit time of a multivariate random walk and its embedding in a quasi-Poisson process, Stoch Anal and Applications (with A. Liew), 24 (2006), 451-474.
On fluctuations of a multivariate random walk with some applications to stock options trading and hedging (with A. Liew), Math. and Comp. Modeling, 44:10 (2006), 931-944.
Hybrid queueing systems with hysteretic bilevel control policies (with S. Kim and L. Tadj), Nonlin Analysis, 65:11 (2006), 2153-2168.
On level crossings of an oscillating marked random walk (with A. Liew), Comp. and Mathematics with Appl., 52 (2006), 917-932.
On exit times of a multivariate random walk with some applications to finance, Nonlin Analysis, 63, 569-577, 2005.
New fluctuation analysis of D-policy bulk queues with multiple vacations, Mathematical and Computer Modeling (with R. Agarwal), 41 (2005), 253-269.
On multivariate delayed recurrent processes, PanAmerican Journ Math (with R. Agarwal), 15:3 (2005), 35-49.
Random observations of marked Cox processes. Time insensitive functionals, Journal Mathematical Analysis and Applications (with R. Agarwal and D. O'Regan), 293 (2004), 1-13
"Fluctutations of recurrent processes and their applications to the stock market," Stoch Anal and Applications, (2004) 22:1.
Time sensitive functionals of marked Cox processes, Journ Math Anal and Applications (with R. Agarwal and D. O'Regan), 293 (2004), 14-27.
Generalized modulated random measures and their potentials, Stoch Anal and Applications (with R. Agarwal and D. O'Regan), 22:4 (2004), 971-988.
A versatile stochastic reliability model with reserve and super-reserve machines, Meth and Computing in Appl Probab (with S-K. Kim), 5:1, 2003 (59-84).
Stochastic disaster recovery systems with external resources, Math and Comp Modeling (with S-K. Kim), 36, 2002 (1235-1257).
Time dependent analysis of multivariate marked renewal processes, J. Appl. Prob. (2001) 38:3.
On functionals of a marked Poisson process observed by a renewal process, Intern. Journ. Math. and Math. Sciences (with Jean-Baptiste Bacot), 24, 2001.
On a bulk input queueing system with batch gated service and multiple vacation policy, Computers Math. Appl., 35, 2001 (with J.-B. Bacot).
Bulk input queues with hysteretic control, Queueing Sys. (with E. Dikong), 32, 287-304, 1999.
Queueing processes in bulk systems under D-policy, Journ. Appl. Prob., 35, 976-989, 1999.
On intensities of modulated Cox measures, Ryszard Syski Special Issue JAMSA, 11:3, 1998.
Queues with hysteretic control by vacation and post-vacation periods. Queueing Systems, 29, 231-268, 1998.
On the level crossing of multidimensional delayed renewal processes, in: Special Issue STOCHASTIC SYSTEMS, JAMSA, 10:4 (1997), 355-361.
Ergodic theorems for modulated stochastic processes, in: Proceeding of the First International Congress of Nonlinear Analysts '92, Walter de Gruyter, Berlin, 1745-1755, 1996.
On termination time processes, in: Studies in Applied Probability; Essays in honour of Lajos Takacs (ed.'s J. Galambos and J. Gani), Applied Probability Trust, Sheffield, U.K., 325-336, 1994.
First excess level analysis of random processes in a class of stochastic servicing systems with global control, Stoch. Anal. Appl., 12:1, 75-101, 1994.
A queueing system with random server capacity, Queueing Sys. (with L. Tadj), 1994.
On applications of first excess random processes to queueing systems with random server capacity and capacity dependent service time, Stochastics and Stochastic Reports, 45, 45-60, 1993 (with L. Tadj).
Stochastic analysis of a control bulk queueing system with continuously operating server: continuous time parameter queueing process, Prob. Stat. Letters, 16:1, 121-128, 1993 (with L. Abolnikov and A. Dukhovny).
Semi-regenerative analysis of controlled bulk queueing systems with a bilevel service delay discipline and some ergodic theorems, Computers Math. Appl., 25:3, 107-116, 1993 (with L. Abolnikov).
Single-server queues with with controlled bulk service, random accumulation level, and modulated input, Stoch. Anal. Appl., 11:1, 29-41, 1993.
A multilevel control bulk queueing system with vacationing server, Oper. Res. Letters, 13, 183-188, 1993 (with L. Abolnikov and A. Dukhovny).
On a single-server queue with fixed accumulation level, state dependent service, and semi-Markov modulated input flow, Int. J. Math. and Math. Sci., 15:3, 593-600, 1992 (with G. Russell)
Ergodicity conditions and invariant probability measure for an embedded Markov chain in a controlled bulk queueing system with a bilevel service delay discipline. Part I, Applied Math. Letters, 5:4, 25-27, 1992 (with L. Abolnikov).
Ergodicity conditions and invariant probability measure for an embedded Markov chain in a controlled bulk queueing system with a bilevel service delay discipline. Part II, Applied Math. Letters, 5:5, 15-18, 1992 (with L. Abolnikov).
On single-server closed queues with priorities and state dependent parameters, Queueing Sys., 8, 237-254, 1991.
On some queue length controlled stochastic processes, J. Appl. Math. Stoch. Anal., 3:4, 227-244, 1990 (with L. Abolnikov and A. Dukhovny).
Multi-channel queueing system with controlled input and state-dependent service, Journ. Appl. Prob., 26:2, 345-362, 1989.
On a duality principle in processes of servicing machines with double control, Journ. Appl. Math. Simulation, 1:3, 245-252, 1988.
Infinite channel queueing system with state-dependent input, Math. Oper. Res., 12:4, 665-677, 1987.
On the multiserver queue with finite waiting room and controlled input, Adv. Appl. Prob., 17 (1985), 408-423.
Recognition & Awards
As a sole PI, Dr. Dshalalow was singly awarded by the National Science Foundation, National Security Agency, and US Army. He was nominated several times for academic and research excellence. He was also a co-PI in one National Science Foundation award. Dr. Dshalalow has also been a participant of joint biomath research teams, awarded by the National Science Foundation.
Dr. Dshalalow published 122 research articles as well as four books. He developed the theory of first excess-level processes, used in stochastic finance, game theory, queueing, established consistency of stochastic estimators of mutation rates of cells, and established ergodic theorems for modulated random measures, which are used in telecommunications, stochastic processes and queueing theory with random perturbations.
Dr. Dshalalow is currently involved in research on strategic defense of stochastic networks, antagonistic stochastic games, applications of stochastics in biology including cancer research, modulated random measures, and stochastiic finance.