@conference {
	title = {Local Stochastic Models in Large Scale Stochastic Hamiltonian Systems},
	author = {Blankenship,  Gilmer L., Baras, John S.},
	year = {1982},
	month = {10/1982},
	abstract = {We consider the problem of isolating the dynamical behavior of a portion of a system imbedded in a large stochastic system. The large scale system is assumed to have a Hamiltonian structure. The method employed is the derivation of the appropriate master equations. Several examples illustrate the theory.},
	address = {Virginia Beach, Virginia},
	booktitle = {The IEEE International Symposium on Large Scale Systems},
	pages = {pp. 474-478}
}
@conference {
	title = {Accurate Evaluation of Stochastic Wiener Integrals with Applications to Scattering and Nonlinear Filtering Problems},
	author = {Hopkins, William E., Blankenship,  Gilmer L., Baras, John S.},
	year = {1982},
	month = {01/1982},
	abstract = {Using s one approximation formulas for stochastic Wiener function Space integrals , it is possible to approximate~the~conditional densities which arise in the nonlinear filtering of diffusion processes to within O(n), with n \&gt;= 1 arbitrary, by n-fold ordinary integrals. The latter have the simple form of a {\textquoteright}rectangular rule", but their accuracy is an order of magnitude better . Then {\textendash} fold integral. can be further decomposed into a recursion involving in one dimensional integrals. The sequence is recursive in the increments of the observation process~in the filtering problem . It is not, however , recursive in time. The one dimensional integrals are naturally treated by an m - step Gaussian quadrature which has an error proportiona1 to nm! / 2" (2 m) : ). (The proportionality constant can be estimated and optimized. ) The computation of these individual integrals can be reduced further by exploiting~certain inherent symmetries of the problem, and by doing some preliminary, {\textquoteright}off-line{\textquoteright} computing. The end result is a highly accurate, computationally efficient numerical algorithm for ~evaluating conditional densities for a substantial class of non linear filtering problems . By accepting light reductions~in accuracy , One can Obtain an algorithm (apparently) fast enough, when efficiently coded, for "Online" recursive filtering in real-time~},
	address = {Shanghai, Peoples Republic of China, Gordon and Breach, New York},
	booktitle = {Recent Developments in Control Theory and its Applications, Proceedings of IEEE--Chinese Association for Automation, Bilateral Meeting on Control Systems},
	pages = {pp. 54-68}
}
@article {
	title = {Accurate Evaluation of Stochastic Wiener Integrals with Applications to Scattering and Nonlinear Filtering Problems},
	author = {Blankenship,  Gilmer L., Baras, John S.},
	year = {1981},
	month = {01/1981},
	abstract = {In 1973 A. J. Chorin [Math. Comp., 27 (1973), pp. 1-15] reported quadrature formulas for the approximation~of a class of Wiener path integrals by n-fold ordinary integrals with an error O(n-2). Similar formulas are presented here for certain stochastic Wiener function space integrals in which n-fold integral approximations result in error O(n^-2) or O(n^-3/2). Stochastic Wiener integrals arise in the physics of wave propagation in random media and in signal estimation problems in communication theory. The present formulas provide simple, accurate computational tools for these applications, among others. This point is illustrated by several examples in the paper.},
	pages = {pp. 518-552},
	volume = {Vol.  41},
	number = {3},
	journal = {SIAM Journal on Applied Mathematics}
}
@conference {
	title = {Nonlinear Filtering of Diffusion Processes},
	author = {Baras, John S., Blankenship,  Gilmer L., S. K. Mitter},
	year = {1981},
	month = {07/1981},
	abstract = {Representations of conditional statistics (densities) are~described for the problem of nonlinear estimation of diffusion processes. Existence and uniqueness properties and algebraic structure of the Duncan-Mortensen-Zakai evolution equation are considered together with some approximation techniques.},
	address = {Kyoto, Japan},
	booktitle = {8th IFAC World Conference},
	pages = {pp. 57-62}
}
@conference {
	title = {Nonlinear Filtering of Diffusion Processes: A Generic Example},
	author = {Blankenship,  Gilmer L., Baras, John S.},
	year = {1979},
	month = {12/1979},
	abstract = {An analytical procedure is described for~ treating a generic nonlinear filtering problem.},
	address = {Ft. Lauderdale, Florida},
	booktitle = {18th IEEE Conference on Decision and Control}
}
@conference {
	title = {On the Conditional Density Equation in Nonlinear Filtering Problems},
	author = {Blankenship,  Gilmer L., Baras, John S.},
	year = {1979},
	month = {06/1979},
	abstract = {We consider the unnormalized conditional density equation arising from a very simple, albeit nontrivial, nonlinear filtering problem. After establishing existence and uniqueness of solutions for this stochastic partial differential equation, we derive an expression for the solution as a "doubly~stochastic{\textquoteright}{\textquoteright} Feynnnann - Kac path integral. The results are extensions of previous results by Pardoux, Chow and others, in that certain operators appearing in this stochastic partial differential equation are unbounded. We then consider the problem of computing the requisite Wiener integral in exact or approximate form. In a different direction an {\textquoteright}{\textquoteright}assumed density{\textquoteright}{\textquoteright} approximation method is applied to this specific stochastic p. d. e. Certain relations with quantum filtering problems are discussed and the possibility of a direct {\textquoteright}distributed{\textquoteright} implementation is investigated. Finally we show how by appropriate nonlinear transformations, these ideas and techniques can be extended to an interesting class of nonlinear filtering problems with multiplicative noise.},
	address = {Grignano, Italy},
	booktitle = {1979 IEEE International Symposium on Information Theory},
	pages = { p. 97}
}
@article {
	title = {Existence, Uniqueness and Asymptotic Behavior of Solutions to a Class of Zakai Equations with Unbounded Coefficients},
	author = {Baras, John S., Blankenship,  Gilmer L., Hopkins, William E., Jr. },
	year = {1983},
	month = {02/1983},
	abstract = {Conditions are given to guarantee the existence and uniqueness of solutions to the Zakai equation associated with the nonlinear filtering of diffusion processes. The conditions permit stronger than a polynomial growth of the coefficients and depend instead on the relative growth rates. The results are derived by adapting, through a sequence of exponential transformations, the classical existence and uniqueness theorems for parabolic PDE{\textquoteright}s due to Besala to the "robust" form of the Zakai equation. In this process, we also obtain sharp estimates for the tail behavior of the conditional density. Examples, including observations through a polynomial sensor and estimation of the state of a "bilinear" system, are worked out in detail. Our results are compared to those of Fleming and Mitter, Pardoux, and Sussmann who, among others, have obtained existence and uniqueness theorems for a more limited class of problems by different methods.},
	pages = {pp. 203-214},
	volume = {Vol. 28-2},
	journal = {IEEE Transactions on Automatic Control.}
}
@conference {
	title = {Accurate Evaluation of Conditional Densities in Nonlinear Filtering},
	author = {Hopkins, William E., Blankenship,  Gilmer L., Baras, John S.},
	address = {New York, NY},
	booktitle = {Advances in Filtering and Stochastic Control, W.H. Fleming and L.G. Gorostiza},
	pages = {pp. 54-68}
}
@conference {
	title = {Existence, Uniqueness and Tail Behavior of Solutions to Zakai Equations with Unbounded Coefficients},
	author = {Hopkins, William E., Baras, John S., Blankenship,  Gilmer L.},
	abstract = {Conditions are given to guarantee the existence and uniqueness of solutions to the Duncan-Mortensen-Zakai equation for nonlinear filtering of multivariable diffusions with unbounded coefficients. Sharp upper and lower bounds on the trail of conditional densities are also obtained. A methodology is described to treat these problems using classical p.d.e methods applied to the "robust" version of the DMZ equation. Several examples are included.},
	address = {New York, NY},
	booktitle = {Advances in Filtering and Stochastic Control, W.H. Fleming and L.G. Gorostiza},
	pages = {pp. 01-17}
}
