Probability, Random Processes, Stochastic Analysis. Applications: Risk Modeling in Actuarial Science and Finance, Queueing Theory, Dynamic Network Reliability, Random Graphs, Path Integrals, Quantum Mechanics.
Publications of Andrzej Korzeniowski
[1] Bounds for Reliability in the NBU, NWU, NBUE, NWUE Classes (with A. Opawski) Applicationes Math., 15 (1976), 1-5.
[2] Martingales in Banach Spaces for which the Convergence with Probability One in Probability and in Law Coincide, Colloquium Mathematicum, 39 (1978), 153-159.
[3] An Analog of Ito and Nisio’s Theorem for Weak Martingales in Banach Spaces Bulletin de L’Académie Polonaise des Sciences, 26 (1978), 1027-1034.
[4] On the Law of the Iterated Logarithm in Banach Spaces Bulletin de L’Académe Polonaise des Sciences, 26 (1978), 1035-1040.
[5] A Proof of the Ergodic Theorem in Banach Spaces via Asymptotic Martingales Bulletin de L’Académie Polonaise des Sciences, 26 (1978), 1041-1044.
[6] Orthogonality and the Law of Large Numbers in Banach Spaces Bulletin de L’Académie Polonaise des Sciences, 27 (1979), 737-743.
[7] Embedding L1 into a non-order Dentable Banach Lattice Bulletin de L’Académie Polonaise des Sciences, 29 (1981), 561-567.
[8] A Remark on Marcinkiewicz SLLN in Banach Spaces Annals of Probability, 12 (1984), 279-280.
[9] Bound State Problem for Random Potentials Stochastic Analysis and Applications, 2 (1984), 121-131.
[10] On the Best Hausdorff-Young Inequality Libertas Mathematica, 4 (1984), 15-19.
[11] An Example in the Theory of Hypercontractive Semigroups (with D. W. Stroock) Proceedings of the AMS, 94 (1985), 87-90.
[12] Dynamic Systems Driven by Markov Processes Journal of Mathematical Physics, 26 (1985), 2189-2191.
[13] On Logarithmic Sobolev Constant for Diffusion Semigroups Journal of Functional Analysis, 71 (1987), 363-370.
[14] A Limit Theorem for Basic Disordered Structures Journal of Mathematical Physics, 28 (1987), 1030-1031.
[15] On Principal Eigenvalue for Random Evolutions (with R. J. Griego) Stochastic Analysis and Applications, 7 (1989), 35-45.
[16] On Diffusions that Cannot Escape from a Convex Set Statistics and Probability Letters, 8 (1989), 229-234.
[17] Solution Algorithm for Parabolic Equation by Simulating Stochastic Processes (with G. J. Fix) Numerical Methods in Partial Diff. Equations, 6 (1989), 185-193.
[18] Asymptotics for Certain Wiener Integrals Associated with Higher Order Differential Operators (with R.J. Griego) Pacific Journal of Mathematics, 14 (1990), 1-8.
[19] A Probabilistic Approach to Numerical Solution of the Nonlinear Diffusion Equation Numerical Methods in Partial Differential Equations, 6 (1990), 335-342.
[20] On simulating Wiener Integrals and their Expectations (with D. L. Hawkins) Probability in the Engineering and Informational Sciences, 5 (1991), 101-112.
[21] Probabilistic Viscosity Algorithm for the Scalar Conservation Law Numerical Methods in Partial Differential Equations, 8 (1992), 277-290.
[22] A Remark on Logarithmic Sobolev Constant Libertas Mathematica, 12 (1992), 9-13.
[23] Quantum Mechanical Simulation of the Hydrogen Molecule Computers and Math. with Applications, 24 (1992), 99-102.
[24] Feynman-Kac Path-Integral Calculation of the Ground-State Energies of Atoms (with J. L. Fry, D. E. Orr and N. G. Fazleev), Phys. Rev. Letters, 69 (1992), 893-896.
[25] Korzeniowski et al. Reply, Physical Review Letters, 71 (1993), 2160-2161.
[26] Numerical Studies of Microturbulence in Water (with D. Greenspan) Computers and Math. with Applications, 29 (1995), 7-15.
[27] Microscopic Turbulence in Water (with D. Greenspan) Mathematical and Computer Modelling, 23 (1996), 89-100.
[28] On Computer Simulation of Feynman-Kac Path- Integrals Journal of Computational and Applied Mathematics, 66 (1996), 333-336.
[29] Application of the Feynman-Kac Path Integral Method in finding the Ground State of Quantum Systems (with J. M. Rejcek, S. Datta, N. G. Fazleev, J. L. Fry), Comp. Phys. Comm., 105 (1997), 108-126.
[30] Path – Integral Calculations for the Excited States of Hydrogen Atom Methodology and Computing in Applied Probability, 1 (1999), 277-282.
[31] On Quantum Mechanical Particle Simulation Proceedings of the International Conference on Monte Carlo Simulation, Balkema Publishers, (2001), 243-246.
[32] On Euler’s Königsberg Bridge Problem for Random Graphs Journal of Propagation in Probability and Statistics, 2 (2001), 11-18.
[33] Computing Quantum states of Atoms through Stochastic Dynamics of Electrons International Journal of Computational and Numerical Analysis and Applications, 1 (2002), 81-87.
[34] On Universal Representation of Random Graphs Annals of Combinatorics, 7 (2003), 299-313.
[35] Binomial Tails Domination for Random Graphs via Bell Polynomials Journal of Probability and Statistical Science, 4 (2006), 99-105.
[36] A discrete Time Counterpart of the Black-Scholes Bond Replication Portfolio Applications and Applied Mathematics, 1 (2006), 25-35.
[37] Mean Reversal for Stochastic Hybrid Systems Nonlinear Analysis: Hybrid Systems, 2 (2008), 613-625.
[38] Stability of Stochastic Differential Equations under Discretization Stochastic Analysis Analysis and Applications, 26 (2008), 1267-1273.
[39] On Mathematical Modeling of Hybrid Network Dynamics under Random Perturbations (with G.S. Ladde) Nonlinear Analysis: Hybrid Systems, 3 (2009), 143-149.
[40] Large Deviations for Additive Functionals of Markov Processes (with A. Oprisan) International Journal of Pure and Applied Mathematics, 53 (2009), 441-459.
[41] Large Deviations for Ergodic Processes in Split Spaces (with A. Oprisan) Dynamic Systems and Applications, 18 (2009), 589-604.
[42] Random Networks with Interacting Nodes (with G.S. Ladde) Neural, Parallel & Scientific Computing, 18 (2010), 333-343.
[43] Large Deviations Application to Exit Times for Switched Markov Processes (with A. Oprisan) International Journal of Pure and Applied Mathematics, 69 (2011), 137-149.
[44] Large Deviations via Almost Sure CLT for Functionals of Markov Processes (with A. Oprisan) Stochastic Analysis and Applications, 30 (2012), 933-947.
[45] On Correlated Random Graphs Journal of Probability and Statistical Science, 11 (2013), 43-58.
[46] Optimal Stopping for Perpetual American Forwards under Markovian Switching Regime(with T. Seaquist) International Journal of Pure and Appl. Mathematics, 87 (2013), 559-586.
[47] The American put with an Ornstein-Uhlenbeck model under Markovian switching (with T. Seaquist) Communications in Applied Analysis 17 (2013), 379–394.
[48] On Donsker type Theorem for discretely reflected backward SDEs (with W. Ventura) Dynamics of Continuous, Discrete and Impulsive Systems, Ser. A: Mathematical Analysis, 23 (2016), 195-208.
[49] On Discretely Reflected Backward Stochastic Differential Equations (with W. Ventura) Stochastic Analysis and Applications, 34 (2016), 1-23.
[50] Dynamic Reliability of a Cluster Server (with R. Traylor) International Journal of Statistics and Probability, 5 (2016), 45-51.
[51] Reliability of a Clustered-Task Server under Modulated Correlation (with R. Traylor) International Journal of Statistics and Probability, 6 (2017), 93-105.
[52] M/M/1 Model with Unreliable Service (with J. Patterson) International Journal of Statistics and Probability, 7 (2018), 125-136.
[53] M/M/1 Model with Unreliable Service and a Working Vacation (with J. Patterson) International Journal of Statistics and Probability, 2 (2019), 1-10.
[54] Decomposition of M/M/1 With Unreliable Service and a Working Vacation (with J. Patterson) International Journal of Statistics and Probability, 1 (2020), 63-70.
[55] Adaptive Risk Hedging for Call Options under Cox-Ingersoll-Ross Interest Rates (with N. Ghorbani) Journal of Mathematical Finance, 2020, 10, 697-704. [56] Put Options with Linear Investment for Hull-White Interest Rates (with N. Ghorbani) Journal of Mathematical Finance, 2021, 11, 152-162. [57] Call and Put Option Pricing with Discrete Linear Investment Strategy (with N. Ghorbani), Journal of Mathematical Finance, 2022, 12, 84-96. [58] Discrete Time Risk Models Financed by Random Premiums, Journal of Mathematical Finance, 2022, 12, 126-137.
[59] Ruin Probability for Risk Model with Random Premiums, Journal of Mathematical Finance, 2023, 13, 171-179.
[60] On Wasserstein Distances for Affine Transformations of Random Vectors (with K. Hamm), Foundation of Data Science, to appear.
[61] Transductive t-SNE for Classification and Data Visualization (with J. Balderas, Li Wang, and Ren-cang Li), Pattern Recognition Letters, Elsevier, submitted.