Mathematics

Publications by R. Sowers

Dimensional Reduction of Random Dynamical Systems

• (with J. H. Park and N. Sri Namachchivaya, Dimensional Reduction in Nonlinear Filtering, Nonlinearity 23 (2010), pp. 305-324.
• Averaging of Stochastic Flows: Twist maps and Escape from Resonance, Stochastic Processes and Their Applications 119 (2009), pp. 349---3582.
• Random Perturbations of Canards Journal of Theoretical Probability 21 (2008), pp. 824--889.
• Stochastic Averaging Near Long Heteroclinic Orbits Stochastics and Dynamics 7 (2007), pp. 187--228.
• Random Perturbations of Two-Dimensional Pseudoperiodic Flows Illinois Journal of Mathematics 50 (2006), pp. 853--959.
• A Boundary-Layer Theory for Diffusively Perturbed Transport around a Heteroclinic Cycle Communications on Pure and Applied Mathematics 58 (2005), pp. 30-84
• New Results on Random Perturbations of Pseudoperiodic Flows, in Proceedings of Fifth EUROMECH Nonlinear Dynamics Conference, Eindhoven (the Netherlands) August 7--12, 2005, pp. 755--764.
• Stochastic Averaging near a Homoclinic Orbit with Multiplicative Noise Stochastics and Dynamics 3 (2003), pp. 299-391
• (with S. N. Evans) Pinching and Twisting Markov Processes Annals of Probability 31 (2003), pp. 486--527.
• Stochastic Averaging with a Flattened Hamiltonian: A Markov Process on a Stratified Space (A Whiskered Sphere), Transactions of the American Mathematical Society 354 (2001), pp. 853--900.
• (with N. Sri Namachchivaya) Rigorous Stochastic Averaging at a Center With Additive Noise, Meccanica 37 (2002), pp. 85-114.
• Stochastic averaging near homoclinic orbits via singular perturbations, in Proceedings of the IUTAM Symposium on Nonlinear Stochastic Dynamics, Monticello (IL) August 26 --30, 2002, pp. 83--94.
• On the Tangent Flow of a Stochastic Differential Equation with Fast Drift, Transactions of the American Mathematical Society 353 (2001), pp. 1321-1334.
• (with N. Sri Namachchivaya) Unified Approach for Noisy Nonlinear Mathieu-Type Systems, Stochastics and Dynamics 1 (2001), pp. 405--450.
• (with N. S. Namachchivaya and L. Vedula), Nonstandard Reduction of Noisy Duffing-van der Pol Equation, Dynamical Systems: an International Journal 16 (2001), pp. 223--245.
• (with N. Sri Namachchivaya and L. Vedula), Stochastic averaging on graphs: Noisy Duffing-van der Pol equation, in Stochaos: Stochastic and Chaotic Dynamics in the Lakes (eds. D. Broomhead, E. A. Luchinskaya, P. McClintock and T. Mullin), American Institute of Physics, Woodbury, (NY), 2000, pp. 255--265.

Stochastic Partial Differential Equations

• Hypoelliptic Random Heat Kernels: A Case Study, Proceedings of the American Mathematical Society 129 (2001), pp. 2451-2460.
• Short-Time Geometry of Random Heat Kernels, Memoirs of the American Mathematical Society, Vol. 132, No. 629, March 1998.
• Intermittency-Type Estimates for some Nondegenerate SPDE's, Annals of Probability 23 (1995), pp. 1853-1874.
• (with C. Mueller) Random travelling waves for the KPP equation with noise, Journal of Functional Analysis 128 (1995), pp. 439--498.
• Multidimensional reaction-diffusion equations with white noise boundary perturbations, Annals of Probability 22 (1994), pp. 2071--2121.
• Recent results on the short-time geometry of random heat kernels, Mathematical Research Letters 1 (1994), pp. 663--675.
• (with C. Mueller) Blowup for the heat equation with a noise term, Probability Theory and Related Fields 97 (1993), pp. 287--320.
• Large deviations for a reaction-diffusion equation with non-Gaussian perturbations, Annals of Probability 20 (1992), pp. 504--537.
• Large deviations for the invariant measure of a reaction-diffusion equation with non-Gaussian perturbations, Probability Theory and Related Fields 92 (1992), pp. 393--421.
• (with Mark I. Freidlin) A Comparison of Homogenization and Large Deviations, with Applications to Wavefront Propagation , Stochastic Process and Their Applications 82 (1999), pp. 23--25.
• (with C. Mueller), Travelling Waves for the KPP Equation with Noise, in Stochastic Analysis, Proceedings of the 1993 AMS Summer Research Institute, Cornell University, Ithaca (NY), July 11--30, 1993, Proceedings of Symposia in Pure Mathematics 57 (ed. Mark Pinsky), AMS, Providence, RI (1995), pp. 603--609.
• (with Mark I. Freidlin) Central limit theorem results for a reaction-diffusion equation with fast-oscillating boundary perturbations, in Stochastic Partial Differential Equations and Their Applications, Proceedings of the IFIP WG 7/1 International Conference, University of North Carolina, Charlotte (NC), June 6--8, 1991, Lecture Notes in Control and Information Sciences 176, (eds. B.L. Rozovskii and R.B. Sowers), Springer, New York, NY (1992), pp. 101--112.

Filtering Theory

• (with A.M. Makowski) On the effects of the initial condition in state estimation for discrete-time linear systems, in Advances in Control and Dynamical Systems (ed. C. T. Leondes), Academic Press, Inc. (1993), pp. 325--393.
• (with A.M. Makowski) On the effects of the initial condition in state estimation for discrete-time linear systems, in Advances in Control and Dynamical Systems (ed. C. T. Leondes), Academic Press, Inc. (1993), pp. 325--393.
• (with A.M. Makowski), Discrete--time filtering for linear systems in correlated noise with non--Gaussian initial conditions: Formulas and asymptotics in Robust Control of Linear Systems and Nonlinear Control, Proceedings of the 1989 International Symposium on the Mathematical Theory of Networks and Systems, Amsterdam (The Netherlands), June 1989 (eds. M.A. Kaashoek, J.H. van Schuppen and A.C.M. Ran), Birkhauser Boston Inc., Cambridge, MA (1990), pp. 407--419.
• (with A. M. Makowski) Discrete-time filtering for linear systems in correlated noise with non-Gaussian initial conditions: Asymptotic behavior of the difference between the MMSE and LMSE estimates, IEEE Transactions on Automatic Control AC-37 (1992), pp. 114--120.
• (with A.M. Makowski), Discrete--time filtering for linear systems in correlated noise with non--Gaussian initial conditions: Formulas and asymptotics in Robust Control of Linear Systems and Nonlinear Control, Proceedings of the 1989 International Symposium on the Mathematical Theory of Networks and Systems, Amsterdam (The Netherlands), June 1989 (eds. M.A. Kaashoek, J.H. van Schuppen and A.C.M. Ran), Birkhauser Boston Inc., Cambridge, MA (1990), pp. 407--419.
• (with A.M. Makowski), Discrete--time filtering for linear systems in correlated noise with non--Gaussian initial conditions, in Proceedings of the 23rd Annual Conference on Information Sciences and Systems, The Johns Hopkins University, Baltimore, March 1989, pp. 308--313.
• (with A.M. Makowski), Discrete--time filtering for linear systems in correlated noise with non--Gaussian initial conditions, in Proceedings of the 23rd Annual Conference on Information Sciences and Systems, The Johns Hopkins University, Baltimore, March 1989, pp. 308--313.

Miscellaneous

• Hydrodynamical Limits and Geometric Measure Theory: Mean Curvature Limits from a Threshold Voter Model, Journal of Functional Analysis 169 (1999), pp. 421--455.
• (with Jang-Mei Wu) Thermal Capacity Estimates on the Allen-Cahn Equation, Transactions of the American Mathematical Society 351 (1999), pp. 2553-2567.

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Richard Sowers (Home Page)
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 West Green Street
Urbana, IL 61801
r-sowers@illinois.edu
Telephone: (217) 333-6246