Stochastic analysis, rough path analysis and fractional Brownian motions
By Laure Coutin, Zhongmin Qian. 2002
403 citations recorded by the source corpus.
Subfields: Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/271fa4420ae2f4a8d3cebfbab617ceda89e06fa5
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In Economics and Econometrics
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In Finance
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Citations in the corpus
- A (rough) pathwise approach to a class of non-linear stochastic partial differential equations (2009, background): “…noise For instance, one can take z as (the rough path lift of) fractional Brownian motion with Hurst parameter 1 / 4 < H < 1 / 2, cf. [11] or [18], a regime which is “rougher” than Brownian and notoriously difficult to handle; or a diffusion with uniformly elliptic generator in…”
- Existence and Uniqueness of the Solution of Stochastic Differential Equation Involving Wiener Process and Fractional Brownian Motion with Hurst Index H > 1/2 (2011, positive): “Later the pathwise approach was extended with the help of Lyons’ rough path theory to the case of arbitrary H in [1] where also unique solvability of equations with H > 1/4 was proved.”
- Differential equations driven by Gaussian signals (2007, background): “[7] Laure Coutin and Zhongmin Qian.”
- Semi-martingales and rough paths theory (2005, background): “Let us remark first that any one-dimensional, continuous local martingale M may be written as Mt = B〈M〉t , where B is a Brownian motion and 〈M〉 the quadratic variation of M .”
- Averaging principle for fast-slow system driven by mixed fractional Brownian rough path (2020, result): “ed rough path theory to define the integral with respect to β-Ho¨lder rough path (1 3 < β < 1 2 ). This theory is basically deterministic (see several monographs [8, 9, 22, 23]). Coutin and Qian [4] proved that fBm admits a natural rough path lift in 1/β-variation rough path topology, which was”
- Elements of Stochastic Calculus via Regularization (2006, methodology): “Lyons rough paths theory approach, see for instance [35, 34, 30, 27, 8] has considered in detail the problem of the existence of integrals of the type ∫ t 0 g(X)·dX .”