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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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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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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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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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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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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...
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Optimal Investment-consumption for Partially Observed Jump-diffusions
We deal with an optimal consumption-investment problem under restricted information in a financial market where the risky asset price follows a...
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A branching particle system approximation for nonlinear stochastic filtering
The optimal filter π = { π t , t ∈ [0, T ]} of a stochastic signal is approximated by a sequence { π
t n } of measure-valued processes defined by... -
Insider trading equilibrium in a market with memory
We consider the Kyle-Back model for insider trading, with the difference that the classical Brownian motion noise of the noise traders is replaced by...
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Filtering from PNS2 Sampling
Periodic Nonuniform Sampling of order 2 (PNS2) is defined by two sequences with same period and some delay between them. PNS2 is known to suppress...
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Moment discretization for ill-posed problems with discrete weakly bounded noise
We study moment discretization for compact operator equations in Hilbert space with discrete noisy data. Instead of assuming that the error in the...
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The risk transfer of non-tradable risks under model uncertainty
In the context of model uncertainty, we study the optimal design and the pricing of financial instruments aiming to hedge some of non-tradable risks....
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Strategic insider trading equilibrium: a filter theory approach
The continuous-time version of Kyle’s (Econometrica 53(6):1315–1336,
1985 ) model of asset pricing with asymmetric information is studied, and... -
Markov measures and extended zeta functions
In this paper we study a family of representations of the Cuntz algebras O p where p is a prime. These algebras are built on generators and...