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352
Stochastic Analysis of the Fractional Brownian Motion
 POTENTIAL ANALYSIS
, 1996
"... Since the fractional Brownian motion is not a semimartingale, the usual Itô calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the ItôClark representation formula and the Girsanov theorem for the functionals of a fractional Brownian motio ..."
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Cited by 199 (11 self)
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Since the fractional Brownian motion is not a semimartingale, the usual Itô calculus cannot be used to define a full stochastic calculus. However, in this work, we obtain the Itô formula, the ItôClark representation formula and the Girsanov theorem for the functionals of a fractional Brownian
Multidimensional fractional calculus operators
 International Journal of Mathematical and Statistical Sciences 5
, 1996
"... This paper deals with some multidimensional integral operators involving the Gauss hypergeometric function in the kernel and generating the multidimensional modified fractional calculus operators introduced in [8]. Some mapping properties, weighted inequalities, a formula of integration by parts and ..."
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Cited by 1 (1 self)
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This paper deals with some multidimensional integral operators involving the Gauss hypergeometric function in the kernel and generating the multidimensional modified fractional calculus operators introduced in [8]. Some mapping properties, weighted inequalities, a formula of integration by parts
Stochastic calculus with respect to Gaussian processes
"... In this paper we develop a stochastic calculus with respect to a Gaussian process of the form Bt = ∫ t 0 K(t, s)dWs, whereW is a Wiener process and K(t, s) is a square integrable kernel, using the techniques of the stochastic calculus of variations. We deduce changeofvariable formulas for the inde ..."
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Cited by 151 (12 self)
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In this paper we develop a stochastic calculus with respect to a Gaussian process of the form Bt = ∫ t 0 K(t, s)dWs, whereW is a Wiener process and K(t, s) is a square integrable kernel, using the techniques of the stochastic calculus of variations. We deduce changeofvariable formulas
Calculus of variations with fractional derivatives and fractional
"... Abstract: We prove EulerLagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of RiemannLiouville. Mathematics Subject Classification: 49K05, 26A33 ..."
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Cited by 33 (25 self)
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Abstract: We prove EulerLagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of RiemannLiouville. Mathematics Subject Classification: 49K05, 26A
Variational time discretization of geodesic calculus
, 2012
"... Abstract. We analyze a variational time discretization of geodesic calculus on finite and certain classes of infinitedimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete logarithm, discrete exponential maps, and discrete paralle ..."
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Cited by 3 (2 self)
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Abstract. We analyze a variational time discretization of geodesic calculus on finite and certain classes of infinitedimensional Riemannian manifolds. We investigate the fundamental properties of discrete geodesics, the associated discrete logarithm, discrete exponential maps, and discrete
Fractional ActionLike Variational Problems
, 2008
"... Fractional actionlike variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multidimensional fractional actionlike problems of the calculus of variations. ..."
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Cited by 27 (16 self)
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Fractional actionlike variational problems have recently gained importance in studying dynamics of nonconservative systems. In this note we address multidimensional fractional actionlike problems of the calculus of variations.
Calculus of variations on time scales
 Dynam. Systems Appl
"... ABSTRACT. We introduce a version of the calculus of variations on time scales, which includes as special cases the classical calculus of variations and the discrete calculus of variations. Necessary conditions for weak local minima are established, among them the Euler condition, the Legendre condit ..."
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Cited by 46 (2 self)
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ABSTRACT. We introduce a version of the calculus of variations on time scales, which includes as special cases the classical calculus of variations and the discrete calculus of variations. Necessary conditions for weak local minima are established, among them the Euler condition, the Legendre
Hamiltonian formalisms for multidimensional calculus of variations and perturbation theory
 Proc. of the Congress in the Conference on noncompact variational problems and general relativity in honor of H. Brezis and
, 2001
"... Abstract — In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton’s formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to the quantum field theory, and expound the simplest ..."
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Cited by 24 (4 self)
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Abstract — In a first part we propose an introduction to multisymplectic formalisms, which are generalisations of Hamilton’s formulation of Mechanics to the calculus of variations with several variables: we give some physical motivations, related to the quantum field theory, and expound
Results 1  10
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352