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White Noise Calculus and Nonlinear Filtering Theory
Annals of Probability, 1985 Quite a while ago, \textit{A. V. Balakrishnan} stressed the inadequacies of modeling white noise with a Wiener process [see for example, Appl. Math. Optimization 1, 97-120 (1974; Zbl 0306.90056)] and suggested that white noise be represented by an additive only probability measure. His main concern was the problem of detecting signals.
G Kallianpur, Rajeeva L Karandikar
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RENORMALIZED HIGHER POWERS OF WHITE NOISE (RHPWN) AND CONFORMAL FIELD THEORY [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2006 The Virasoro–Zamolodchikov *-Lie algebra w∞ has been widely studied in string theory and in conformal field theory, motivated by the attempts of developing a satisfactory theory of quantization of gravity. The renormalized higher powers of quantum white noise (RHPWN) *-Lie algebra has been recently investigated in quantum probability, motivated by the
Luigi Accardi, Andreas Boukas
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White noise theory of robust nonlinear filtering with correlated state and observation noises [PDF]
Systems and Control Letters, 1994 This paper deals with the robust nonlinear filtering equations in the correlated observation noise case. In the existing `direct' white noise theory of nonlinear filtering, the state process is still modelled as a Markov process satisfying an Itô stochastic differential equation (which is not robust due to the fact that the set of all possible real ...
Arunabha Bagchi, Rajeeva L Karandikar
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ON QUANTUM THEORY IN TERMS OF WHITE NOISE [PDF]
Nagoya Mathematical Journal, 1977 It has often been pointed out that a much more manageable structure is obtained from quantum theory if the time parameter t is chosen imaginary instead of real. Under a replacement of t by i·t the Schrödinger equation turns into a generalized heat equation, time ordered correlation functions transform into the moments of a probability measure, etc ...
HIDA, T, Streit, Ludwig
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An introduction to white–noise theory and Malliavin calculus for fractional Brownian motion [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2004 The paper presents an introduction to stochastic calculus for fractional Brownian motion with parameter between 0 and 1, with emphasis on stochastic integration based on white noise theory and Malliavin differentiation.
Francesca Biagini +2 more
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Axioms, 2022 In this article, we discuss the (2 + 1)-D coupled Korteweg–De Vries (KdV) equations whose coefficients are variables, and stochastic (2 + 1)-D C-KdV (C-KdV) equations with the χ-Wick-type product.
Mohammed Zakarya +2 more
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Fractal and Fractional, 2023 The qualitative theory for planar dynamical systems is used to study the bifurcation of the wave solutions for the space-fractional nonlinear Schrödinger equation with multiplicative white noise.
Muneerah Al Nuwairan
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Interspike interval correlations in neuron models with adaptation and correlated noise.
PLoS Computational Biology, 2021 The generation of neural action potentials (spikes) is random but nevertheless may result in a rich statistical structure of the spike sequence. In particular, contrary to the popular renewal assumption of theoreticians, the intervals between adjacent ...
Lukas Ramlow, Benjamin Lindner
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Generalized Mehler Semigroup on White Noise Functionals and White Noise Evolution Equations
Mathematics, 2020 In this paper, we study a representation of generalized Mehler semigroup in terms of Fourier–Gauss transforms on white noise functionals and then we have an explicit form of the infinitesimal generator of the generalized Mehler semigroup in terms of the ...
Un Cig Ji, Mi Ra Lee, Peng Cheng Ma
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Outbreak-size distributions under fluctuating rates
Physical Review Research, 2023 We study the effect of noisy infection (contact) and recovery rates on the distribution of outbreak sizes in the stochastic susceptible-infected-recovered model.
Jason Hindes +3 more
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