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A Small Time Approximation for the Solution to the Zakai Equation
We propose a novel small time approximation for the solution to the Zakai equation from nonlinear filtering theory. We prove that the unnormalized...
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Topological phase estimation method for reparameterized periodic functions
We consider a signal composed of several periods of a periodic function, of which we observe a noisy reparametrization. The phase estimation problem...
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A comparison of nonlinear extensions to the ensemble Kalman filter
Ensemble Kalman filters are based on a Gaussian assumption, which can limit their performance in some non-Gaussian settings. This paper reviews two...
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Positive-instantaneous frequency and approximation
Positive-instantaneous frequency representation for transient signals has always been a great concern due to its theoretical and practical...
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Approximations for the Boundary Crossing Probabilities of Moving Sums of Random Variables
In this paper we study approximations for the boundary crossing probabilities of moving sums of i.i.d. normal random variables. We approximate a...
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Ergodicity and Accuracy of Optimal Particle Filters for Bayesian Data Assimilation
Data assimilation refers to the methodology of combining dynamical models and observed data with the objective of improving state estimation. Most...
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Robust Scan Statistics for Detecting a Local Change in Population Mean for Normal Data
In this article we investigate the performance of robust scan statistics based on moving medians, as test statistics for detecting a local change in...
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Fractional Generalizations of Zakai Equation and Some Solution Methods
The paper discusses fractional generalizations of Zakai equations arising in filtering problems. The derivation of the fractional Zakai equation,...
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Intermittency and stochastic pseudo-differential equation with spatially inhomogeneous white noise
In this paper, we study the intermittent property for the following nonlinear stochastic partial differential equation (SPDE in the sequel) in...
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A method for high-dimensional smoothing
We consider the problem of the computation of smoothed additive functional, which are some integrals with respect to the joint smoothing...
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Maximum loss and maximum gain of spectrally negative Lévy processes
The joint distribution of the maximum loss and the maximum gain is obtained for a spectrally negative Lévy process until the passage time of a given...
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Generalized Anderson Model with Time-Space Multiplicative Fractional Noise
We study the existence and the properties of the solution to a stochastic partial differential equation with multiplicative time-space fractional...
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Reconstruction from Periodic Nonstationary Sampling (PNS) without Resampling
Periodic Nonuniform Samplings (PNS) are concatenations of periodic samplings of same periods but which are shifted. They allow to suppress aliasings,...
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Credit Risk in an Economy with New Firms Arrivals
We propose a dynamic model to analyze the credit quality of firms. In the market in which they operate, the firms are divided into a finite number of...
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On robustness of discrete time optimal filters
A new result on stability of an optimal nonlinear filter for a Markov chain with respect to small perturbations on every step is established. An...
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Multiple Window Scan Statistics for Two Dimensional Poisson Processes
In this article, approximations for the distribution of multiple window scan statistics for Poisson Processes on a two dimensional rectangular region...
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Inferences from optimal filtering equation*
The processing of stationary random sequences under nonparametric uncertainty is given by a filtering problem when the signal distribution is...
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Equivalent Circuits for the PNS3 Sampling Scheme
Periodic nonuniform sampling of order three (PNS3) is a sampling scheme composed of three periodic sequences with the same period. It is well-known...
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Data Assimilation in Cardiovascular Fluid–Structure Interaction Problems: An Introduction
Numerical methods for incompressible fluid dynamics have recently received a strong impulse from the applications to the cardiovascular system. In...