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An Approximate Bayesian Approach to Optimal Input Signal Design for System Identification. [PDF]
Entropy (Basel)Bania P, Wójcik A.
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Motion of Quantum Particles in Terms of Probabilities of Paths. [PDF]
Entropy (Basel)Santos E.
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IEEE Transactions on Automatic Control, 2013
The technical note deals with state estimation of nonlinear stochastic dynamic systems. Traditional filters providing local estimates of the state, such as the extended Kalman filter, unscented Kalman filter, or the cubature Kalman filter, are based on computationally efficient but approximate integral evaluations.
Jindrich Duník +2 more
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The technical note deals with state estimation of nonlinear stochastic dynamic systems. Traditional filters providing local estimates of the state, such as the extended Kalman filter, unscented Kalman filter, or the cubature Kalman filter, are based on computationally efficient but approximate integral evaluations.
Jindrich Duník +2 more
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On Stochastic Integration and Differentiation
Acta Applicandae Mathematica, 1999This short note presents a method to identify the integrands \((\varphi_j)_{j=1}^n\) for a martingale \(\xi_t=\sum_{j=1}^n\int_0^t\varphi_j d\eta^j_t\), \((\eta^j)_{j=1}^n\) being independent Brownian motions, in a measurable way. The quintessence of the method is an \(L^2\)-limit of certain approximations to the quadratic covariation between \(\xi ...
Di Nunno, G., Rozanov, Yu. A.
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Stochastic integration with respect to a stochastic integral
Stochastic Analysis and Applications, 1997In this paper we prove first the property of integration with respect to a measure defined by density,h(fm) = (hf)mor a measure mand functions f,h, taking values in Banach spaces. Then we use this result to prove the similar “associativity” property of the stochastic integralL.(K-X)= (LK) Xfor processes X,K,Ltaking values in Banach ...
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A Stochastic Integral Equation
SIAM Journal on Applied Mathematics, 1970We investigate a stochastic integral equation of the form $x'(s) = y'(s) + \int_0^\alpha {K(s,t)dx(t)} $, where $y( s )$ is a process with orthogonal increments on the interval $T_\alpha = [0,\alpha ]$ and $K(s,t)$ is a continuous Fredholm or Volterra kernel on $T_\alpha \times T_\alpha $.
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Stochastic Integrals and Differential Measures
Theory of Probability & Its Applications, 1988The description of the class of measures with square integrable logarithmic derivative along a vector field and an operator field is obtained. This derivative coincides with an extended stochastic integral in the Gaussian case. The proofs are based on integration by parts.
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1990
In this chapter, we define (stochastic) Ito-integrals \(\int_0^t {HdM} \) H dM for local L 2 — martingales M and a fairly large class of adapted processes H. The integral is a random variable. It will be constructed as a suitable limit of Riemann-Stieltjes type approximations like $$\sum\limits_{i = 1}^n {{H_{{s_i}}} \cdot \left( {{M_{s{}_{i + 1}}}
Heinrich von Weizsäcker +1 more
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In this chapter, we define (stochastic) Ito-integrals \(\int_0^t {HdM} \) H dM for local L 2 — martingales M and a fairly large class of adapted processes H. The integral is a random variable. It will be constructed as a suitable limit of Riemann-Stieltjes type approximations like $$\sum\limits_{i = 1}^n {{H_{{s_i}}} \cdot \left( {{M_{s{}_{i + 1}}}
Heinrich von Weizsäcker +1 more
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2015
We have now established enough basic theory to construct the stochastic integral in full generality. In this chapter, we develop the integral with respect to semimartingales, and prove some of its properties. As in the previous chapters, we assume we have a filtered probability space, with filtration satisfying the usual conditions, \(\mathcal{F}_ ...
Samuel N. Cohen, Robert J. Elliott
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We have now established enough basic theory to construct the stochastic integral in full generality. In this chapter, we develop the integral with respect to semimartingales, and prove some of its properties. As in the previous chapters, we assume we have a filtered probability space, with filtration satisfying the usual conditions, \(\mathcal{F}_ ...
Samuel N. Cohen, Robert J. Elliott
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On a Generalization of a Stochastic Integral
Theory of Probability & Its Applications, 1976openaire +2 more sources