Differential equations driven by fractional Brownian motion

By David Nualart, A. Rășcanu. 2002

516 citations recorded by the source corpus.

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Citations in the corpus

Ergodicity of the Infinite Dimensional Fractional Brownian Motion (2011, background): “Meanwhile there are many articles dealing with existence of solutions of ordinary or partial stochastic differential equations driven by a fractional Brownian motion, see for instance [7,10,18,19, 21 ,24] among others.”
Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions (2014, methodology): “This result was first proved by Lyons [14], using Young integrals (see [33]) and p-variation estimates, and later by Nualart and Rascanu [25], using fractional calculus; see [34].”
Fractional stochastic differential equations with applications to finance (2013, background): “In [24] Nualart and Răşcanu have studied stochastic differential equations with respect to fBm with Hurst index H > 1/2.”
Malliavin Calculus for Fractional Delay Equations (2009, methodology): “Introduction The recent progresses in the analysis of differential equations driven by a fractional Brownian motion, using either the complete formalism of the rough path analysis [3, 10, 18], or the simpler Young integration setting [25, 33], allow to study some of the basic properties of the proce”
Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H (2006, unknown): “…for stochastic differential equations (SDEs) driven by a fractional Brownian motion (f Bm) has not yet been established and in fact only a few results have been proved (see for example, Nualart and Rascanu 2002; Nualart and Ouknine 2003; Coutin and Qian 2000) for various approaches to the problem.”
Convergence of delay differential equations driven by fractional Brownian motion (2009, methodology): “The following estimates are proved in [6] (see Proposition 4.”
Functional differential equations in Hilbert spaces driven by a fractional Brownian motion (2012, methodology): “For the proof, we need the following version of the Gronwall lemma proved in [ 8 ].”
Malliavin calculus for stochastic differential equations driven by a fractional Brownian motion (2009, methodology): “Using formula (3), Nualart and Răşcanu have derived the following estimates (see [12], Propositions 4.”
Exact Rate of Convergence of Some Approximation Schemes Associated to SDEs Driven by a Fractional Brownian Motion (2006, background): “The derivative process of F is the element of L 2 (Ω , H ) deﬁned by In particular D s B t = 1 [0 ,t ] ( s ).”
Transportation inequalities for stochastic differential equations driven by a fractional Brownian motion (2012, methodology): “The estimates on the solution (xt)t∈[0,T ] obtained in [25] were improved in [19], Theorem 3.”
Existence and uniqueness of the solution to uncertain fractional differential equation (2015, methodology): “Stochastic fractional differential equations were used to model dynamical systems affected by random noises [9-15].”
Differential Equations Driven by Hölder Continuous Functions of Order Greater than 1/2 (2006, methodology): “Our aim is to obtain estimates on xt which are better than those given by Nualart and Răşcanu in [3].”
Pathwise solutions of SPDEs driven by Hölder-continuous integrators with exponent larger than $1/2$ and random dynamical systems (2013, methodology): “When the driving process is a Hölder continuous function with Hölder exponent greater than 1/2, a different technique to solve these equations consists of using fractional calculus tools, see for example the papers [6, 13, 14, 17, 19, 21], to name only a few of them.”
The rate of convergence for Euler approximations of solutions of stochastic differential equations driven by fractional Brownian motion (2007, methodology): “We use here the growth and Hölder estimates of solution of corresponding pathwise equations from the paper [10].”