Knut SolnaAssistant Professor, Mathematics |
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Research Interests |
Applied mathematics, applied probablility, stochastic differential equations, mathematical finance, waves in random media, time reversal methods | |
| URL | Home page with link to papers. | |
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Academic Distinctions |
Sloan Fellowship 2004-2006 Instructorship award at the University of Utah 1998. Fulbright Award 1990 |
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| Appointments | Wylie Instructor, Department of Mathematics, University of Utah, 1997-2000. | |
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Research Abstract |
Modeling and analysis of problems described by partial differential equations with heterogeneous and random coefficients. Analysis of waves propagating through multiscale and heterogeneous media with applications to seismology, remote sensing and communication through the turbulent atmosphere. Applications to pricing theory for financial instruments in volatile and multiscale markets. |
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| Publications | S. Hou, K. Solna and H. Zhao, Imaging of Location and Geometry for Extended Targets Using the Response Matrix, Accepted for publication in Journal of Computational Physics. | |
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J.P. Fouque, G. Papanicolaou, R. Sircar and K. Solna, Timing the Smile, Accepted for publication in The Wilmott Magazine 2004. |
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A. Fannjian and K. Sona, Scaling limits for beam wave propagation in atmospheric turbulence, Accepted for publication in Stochastics and Dynamics 2004. |
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| J.P. Fouque and K. Solna, Time-reversal aperture enhancement, SIAM Journal on Multiscale Modeling and Simulation, 2003. | ||
| A. Nachbin and K. Solna, Apparent diffusion due to mountain microstructure in shallow waters, Physics of Fluids, V 15, 1, 66 -77, 2003. | ||
| K. Solna, Acoustic pulse spreading in a random fractal, SIAM Journal on Applied Mathematics, 2003. | ||
| J.P. Fouque, G. Papanicolaou, K.R. Sircar and K. Solna, Short time scales in S&P500 volatility, The Journal of Computational Finance, V 6, 4, 1--24, 2003. | ||
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J.P. Fouque, G. Papanicolaou, K.R. Sircar and K. Solna, Singular perturbations in option pricing, SIAM Journal on Applied Mathematics, 2003. |
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| G. Papanicolaou, L. Ryzhik and K. Solna, Statistical stability in time reversal, SIAM Journal on Applied Mathematics, 2003. | ||
| J.P. Fouque, G. Papanicolaou, K.R. Sircar and K. Solna, Maturity Cycles in Implied Volatility, Finance and Stochastics, 2003. | ||
| J.P. Fouque, G. Papanicolaou, K. R. Sircar and K. Solna, Multiscale Stochastic Volatility Asymptotics, SIAM Journal on Multiscale Modeling and Simulation, 2003. | ||
| K. Solna and G. Milton, Can mixing materials make electromagnetic signals travel faster?, SIAM Journal on Applied Mathematics, V 62, 6, 2064-2091, 2002. | ||
| G.C. Papanicolaou and K. Solna, Wavelet based estimation of Kolmogorov turbulence, In: Long-range Dependence: Theory and Applications, P. Doukhan, G. Oppenmeim and M.S. Taqqu, editors, Birkhauser, 2002. | ||
| K. Solna, Focusing of time-reversed reflections, Waves in Random Media, V 10, 151 -- 198, 2002. | ||
| Grant | National Science Foundation (NSF), The Office of Naval Research (ONR), The Defense Advanced Research Projects Agency (DARPA), Airforce Office of Scientific Research (AFOSR). | |
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Professional Societies |
SIAM, Society for Industrial and Applied Mathematics. AMS, American Mathemaical Society. SEG, Society of Exploration Geophysicists. |
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| Link to this profile | http://www.faculty.uci.edu/profile.cfm?faculty_id=4954 | |
| Last updated | 02/18/2004 | |