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29
ConditionalMean Estimation Via JumpDiffusion Processes in Multiple Target Tracking/Recognition
 IEEE TRANSACTIONS ON SIGNAL PROCESSING
, 1995
"... A new algorithm is presented for generating the conditional mean estimates of functions of target positions, orientations and type in recognition, and tracking of an unknown nmnber of targets and target types. Taking a Bayesian approach, a posterior measure is defined on the tracking/target paramete ..."
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Cited by 28 (5 self)
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A new algorithm is presented for generating the conditional mean estimates of functions of target positions, orientations and type in recognition, and tracking of an unknown nmnber of targets and target types. Taking a Bayesian approach, a posterior measure is defined on the tracking/target parameter space by combining a narrowband sensor array manifold model with a high resolution imaging model, and a prior based on airplane dynanfics. The Newtoninn force equations governing rigid body dynamic s are utilized to form the prior density on airplane motion. The conditional mean estimates are generated using a random sampling algorithm based on jumpdiffusion processes [1] i)r empirically generating MMSE estimates of functions of these random target positions, orientations, and type under the posterior measure. Results are presented on target tracking and identification from an implementation of the algorithm on a networked Silicon Graphics workstation and DECmpp/MasPar parallel machine.
Carlo Optimization and Path Dependent Nonstationary
 Laws of Large Numbers, IIASA Interim Report IR98009
, 1998
"... review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. –ii– New types of laws of large numbers are derived by using connections between estimation and stochastic optimization probl ..."
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Cited by 7 (2 self)
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review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. –ii– New types of laws of large numbers are derived by using connections between estimation and stochastic optimization problems. They enable one to “track ” timeandpath dependent functionals by using, in general, nonlinear estimators. Proofs are based on the new stochastic version of the second Lyapunov’s method. Applications to adaptive MonteCarlo optimization, stochastic branch and bounds method and minimization of risk functions are discussed. – iii–
Multidimensional Version Of A Result Of Sakhanenko In The Invariance Principle For Vectors With Finite Exponential Moments
 IIII, Theory Probab. Appl
, 1998
"... . A multidimensional version of a result of Sakhanenko for the Gaussian approximation of sequences of successive sums of independent nonidentically distributed random vectors with finite exponential moments is obtained. 1. Introduction The aim of this paper is to give a multidimensional generaliza ..."
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Cited by 7 (0 self)
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. A multidimensional version of a result of Sakhanenko for the Gaussian approximation of sequences of successive sums of independent nonidentically distributed random vectors with finite exponential moments is obtained. 1. Introduction The aim of this paper is to give a multidimensional generalization of a result of Sakhanenko (1984) which is an extension and sharpening of the famous result of Koml'os, Major and Tusn'ady (KMT) (197576) to the case of nonidentically distributed random variables. For formulations of results we need the following notation. Notation 1.1. We write z 2 R d (or C d ), if z = (z 1 ; : : : ; z d ) = z 1 e 1 + \Delta \Delta \Delta + z d e d , where z j 2 R 1 (or C 1 ) and the e j are the basis vectors. The scalar product of vectors x; y 2 R d (or C d ) is denoted by\Omega x; y ff = x 1 y 1 + \Delta \Delta \Delta +x d y d . For z 2 R d (or C d ) we use the Euclidean norm kzk =\Omega z; z ff 1=2 and the maximum norm jzj = max 16j6k ...
On Weak Solutions of Backward Stochastic Differential Equations
"... The main objective of this paper consists in discussing the concept of weak solutions of a certain type of backward stochastic differential equations. Using weak convergence in the MeyerZheng topology, we shall give a general existence result. The terminal condition H depends in functional form o ..."
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Cited by 5 (0 self)
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The main objective of this paper consists in discussing the concept of weak solutions of a certain type of backward stochastic differential equations. Using weak convergence in the MeyerZheng topology, we shall give a general existence result. The terminal condition H depends in functional form on a driving cdlg process X , and the coefficient f depends on time t and in functional form on X and the solution process Y . The functional f(t; x; y); (t; x; y) 2 [0; T ] D [0; T ]; R , is assumed to be bounded and continuous in (x; y) on the Skorohod space D [0; T ]; R in the MeyerZheng topology. By several examples of Tsirelson type, we will show that there are, indeed, weak solutions which are not strong, i.e., are not solutions in the usual sense. We will also discuss pathwise uniqueness and uniqueness in law of the solution and conclude, similar to the Yamada Watanabe theorem, that pathwise uniqueness and weak existence ensure the existence of a (uniquely determined) strong solution. Applying these concepts, we are able to state the existence of a (unique) strong solution if, additionally to the assumptions described above, f satisfies a certain generalized Lipschitz type condition. 1
The stochastic goodwill problem
 European Journal of Operational Research
, 2003
"... Utility maximization problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the ..."
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Cited by 5 (1 self)
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Utility maximization problems related to optimal advertising under uncertainty are considered. In particular, we determine the optimal strategies for the problem of maximizing the utility of goodwill at launch time and minimizing the disutility of a stream of advertising costs that extends until the launch time. We also consider some generalizations such as problems with constrained budget, optimization under partial information, and discretionary launching. Key Words: advertising, linear quadratic regulator, new product introduction, stochastic control, utility maximization.
Robustness and Convergence of Approximations to Nonlinear Filters for JumpDiffusions
 Computational and Applied Math
, 1996
"... The paper treats numerical approximations to the nonlinear filtering problem for jumpdiffusion processes. This is a key problem in stochastic systems analysis. The processes are defined, and the optimal filters described. In the general nonlinear case, the optimal filters cannot be computed, and s ..."
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Cited by 4 (2 self)
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The paper treats numerical approximations to the nonlinear filtering problem for jumpdiffusion processes. This is a key problem in stochastic systems analysis. The processes are defined, and the optimal filters described. In the general nonlinear case, the optimal filters cannot be computed, and some numerical approximation is needed. Then the weak conditions that are required for the convergence of the approximations are given and the convergence is proved. Examples of useful approximations which satisfy the conditions are given. Quite weak conditions are given under which the approximating filter is continuous in the observation function, and it is shown that our canonical methods satisfy the conditions. Such continuity is essential if the approximations are to be used with confidence on actual physical data. Finally, we prove the convergence of monte carlo methods for approximating the optimal filters, and also show that the optimal filter is continuous in the parameters of the si...
On Derivations and Solutions of Master Equations and Asymptotic Representations
, 1978
"... A linear semigroup for both: Markov processes and nonMarkov processes as they occur in the description of macroscopic systems is introduced. The elegance of the semigroup approach is demonstrated by the derivation of the master equation for a Markov process which undergoes continuous and discontin ..."
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Cited by 4 (0 self)
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A linear semigroup for both: Markov processes and nonMarkov processes as they occur in the description of macroscopic systems is introduced. The elegance of the semigroup approach is demonstrated by the derivation of the master equation for a Markov process which undergoes continuous and discontinuous jumps. By use of nonlinear transformations of stochastic processes a class of processes is found for which the whole stochastic kinetics reduces mainly to the kinetics of a general GaussMarkov process. Further the convergence of sequences of Markov processes to a limiting Markov process is studied. In this context, a semigroup formulation for the validity of various expansion methods of master equations developed recently is given and the convergence of functionals of the original process to a limiting transformed process is investigated. Some results are illustrated for the behaviour of the stochastics in a bistable tunnel diode. A model for macroscopic irreversibility is introduced using a sequence of nonMarkov processes which converges to a FokkerPlanck process. Finally a few accomplishments on some recent related works are given.
JumpDiffusions With Controlled Jumps: Existence and Numerical Methods
 Methods, J. Math. Anal. Applic
, 2000
"... A comprehensive development of effective numerical methods for stochastic control problems in continuous time, for reflected jumpdiffusion models, is given in [10, 11, 16]. While these methods cover the bulk of models which have been of interest to date, they do not explicitly deal with the cas ..."
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Cited by 3 (1 self)
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A comprehensive development of effective numerical methods for stochastic control problems in continuous time, for reflected jumpdiffusion models, is given in [10, 11, 16]. While these methods cover the bulk of models which have been of interest to date, they do not explicitly deal with the case where the jump itself is controlled in the sense that the value of the control just before the jump affects the distribution of the jump. We do not deal explicitly with the numerical algorithms but develop some of the concepts which are needed to provide the background which is necessary to extend the proofs of [10, 11, 16] to this case. A critical issue is that of closure: i.e., defining the model such that any sequence of (systems, controls) has a convergent subsequence of the same type. One needs to introduce an extension of the Poisson measure (which serves a purpose analogous to that served by relaxed controls), which we call the relaxed Poisson measure, analogously to the us...
STABILITY OF JACKSONTYPE QUEUEING NETWORKS, I
, 1999
"... This paper gives a pathwise construction of Jacksontype queueing networks allowing the derivation of stability and convergence theorems under general probabilistic assumptions on the driving sequences; namely, it is only assumed that the input process, the service sequences and the routing mechanis ..."
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This paper gives a pathwise construction of Jacksontype queueing networks allowing the derivation of stability and convergence theorems under general probabilistic assumptions on the driving sequences; namely, it is only assumed that the input process, the service sequences and the routing mechanism are jointly stationary and ergodic in a sense that is made precise in the paper. The main tools for these results are the subadditive ergodic theorem, which is used to derive a strong law of large numbers, and basic theorems on monotone stochastic recursive sequences. The techniques which are proposed here apply to other and more general classes of discrete event systems, like Petri nets or GSMP’s. The paper also provides new results on the Jacksontype networks with i.i.d. driving sequences which were studied in the past.