Results 31 to 40 of about 1,064 (85)
Quantum Stochastic Cable Equation Acting on Functionals of Discrete‐Time Normal Martingales
Advances in Mathematical Physics, Volume 2019, Issue 1, 2019., 2019 Let M be a discrete‐time normal martingale satisfying some mild conditions. Then Gel’fand triple S(M)⊂L2(M)⊂S⁎(M) can be constructed of functionals of M, where elements of S(M) are called testing functionals of M, while elements of S⁎(M) are called generalized functionals of M.
Yuling Tang +4 more
wiley +1 more source
Interacting Stochastic Process and Renormalization Theory
, 2000 A stochastic process with self-interaction as a model of quantum field theory is studied. We consider an Ornstein-Uhlenbeck stochastic process x(t) with interaction of the form x^{(\alpha)}(t)^4, where $\alpha$ indicates the fractional derivative.
Volovich, Yaroslav
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Toward infinite‐dimensional Clifford analysis
Mathematical Methods in the Applied Sciences, Volume 47, Issue 10, Page 8062-8075, 15 July 2024.Clifford analysis is a higher dimensional function theory and a refinement of harmonic analysis. We will extend Clifford analysis to the infinite‐dimensional setting. To do that, we have to introduce infinite‐dimensional Clifford algebras and the infinite‐dimensional Dirac operator.
Swanhild Bernstein
wiley +1 more source
On stochastic differential equations driven by the renormalized square of the Gaussian white noise
, 2015 We investigate the properties of the Wick square of Gaussian white noises through a new method to perform non linear operations on Hida distributions.
Ammou, Bilel Kacem Ben +1 more
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Stochastic Calculus with respect to Gaussian Processes
, 2017 Stochastic integration with respect to Gaussian processes, such as fractional Brownian motion (fBm) or multifractional Brownian motion (mBm), has raised strong interest in recent years, motivated in particular by applications in finance, Internet traffic
Lebovits, Joachim
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Malliavin calculus and optimal control of stochastic Volterra equations
, 2015 Solutions of stochastic Volterra (integral) equations are not Markov processes, and therefore classical methods, like dynamic programming, cannot be used to study optimal control problems for such equations.
Agram, Nacira, Øksendal, Bernt
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Hamiltonian Path Integrals In Momentum Space Representation via White Noise Techniques
, 2013 The concepts of Feynman integrals in white noise analysis are used to construct the Feynman integrand for the harmonic oscillator in momentum space representation as a Hida distribution. Moreover it is shown that in a limit sense, the potential free case
Bock, Wolfgang
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Integral Representation of Generalized Grey Brownian Motion
, 2019 In this paper we investigate the representation of a class of non Gaussian processes, namely generalized grey Brownian motion, in terms of a weighted integral of a stochastic process which is a solution of a certain stochastic differential equation.
Bock, Wolfgang +2 more
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Wick Calculus For Nonlinear Gaussian Functionals
, 2009 This paper surveys some results on Wick product and Wick renormalization. The framework is the abstract Wiener space. Some known results on Wick product and Wick renormalization in the white noise analysis framework are presented for classical random ...
A. Budhiraja +25 more
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A White Noise Approach to Mixed Fractional Brownian Motion [PDF]
, 2010 This paper gives an overview to the mixed fractional Brownian motion in the white noise analysis framework, in particular how to realize and analyze mixed fractional Brownian motion in the white noise space. An application to the Donsker's delta function
Suryawan, Herry Pribawanto
core