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Keywords
(7)
Analytic Semigroup
Evolution Equation
fractional brownian motion
Gaussian Noise
Rough Path Theory
Space Time
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Rough evolution equations
Rough evolution equations,10.1214/08AOP437,Annals of Probability,Massimiliano Gubinelli,Samy Tindel
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Rough evolution equations
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Citations: 20
)
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Massimiliano Gubinelli
,
Samy Tindel
We generalize Lyons’
rough paths
theory in order to give a pathwise meaning to some nonlinear infinitedimensional
evolution equation
associated to an
analytic semigroup
and driven by an irregular noise. As an illustration, we discuss a class of linear and nonlinear 1d SPDEs driven by a space–time
Gaussian noise
with singular space covariance and Brownian time dependence.
Journal:
Annals of Probability  ANN PROBAB
, vol. 38, no. 2010, pp. 175, 2010
DOI:
10.1214/08AOP437
Cumulative
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Citation Context
(9)
...scheme has been applied to fBm in a paper by Coutin and Qian [
4
], by means of standard ndyadic piecewise linear approximations ˜ B 2...
...Both approximation schemes introduced in [
4
,16] (see also the recent preprint [5]) lead to the same semiquantitative result, namely:...
...The extended integral we deal with is based on the notion of increment, together with an elementaryoperator δ actingonthem.Thesefirstnotionsarespecificallyintroducedin[8,
10
], and we shall merely recall here their definition in the complex plane context...
Samy Tindel
,
et al.
The rough path associated to the multidimensional analytic fBm with an...
...The interested reader is sent to [18] for a complete account on the topic, or to [11,
19
] for a more detailed summary...
...We refer to [11,
19
] for two simplified versions...
Aurélien Deya
,
et al.
A Milsteintype scheme without Levy area terms for SDEs driven by frac...
...The present results, together with those in the just appeared preprint [
14
], seem to be the first steps in this direction...
Michael Caruana
,
et al.
Partial differential equations driven by rough paths
...(iii) As in [
8
, 15], we have chosen here to solve the dierential equation (5) thanks to a variant of Lyon’s rough path method [4, 10] called algebraic integration theory, introduced in [6]...
...These first notions are specifically introduced in [6,
8
], and we shall merely recall here their definition in the complex plane context...
...The algebraic integration theory heavily relies on a generalization of Young integrals to increments in C2 (as explained in [6,
8
])...
Samy Tindel
,
et al.
The rough path associated to the multidimensional analytic fbm with an...
...We refer to [7,
12
] for two simplified versions...
...We refer again to [7,
12
] for the proof of these statements...
Aurélien Deya
,
et al.
Rough Volterra equations 1: the algebraic integration setting
References
(25)
Lévy Area of Wiener Processes in Banach Spaces
(
Citations: 31
)
M. Ledoux
,
T. Lyons
,
Z. Qian
The Malliavin calculus and related topics
(
Citations: 840
)
D. Nualart
Published in 1995.
Evolution equations driven by a fractional Brownian motion
(
Citations: 48
)
B. Maslowski
,
D. Nualart
Published in 2002.
Differential equations driven by rough signals
(
Citations: 139
)
T. Lyons
Published in 1998.
Integration with respect to fractal functions and stochastic calculus. I
(
Citations: 185
)
M. Zähle
Journal:
Probability Theory and Related Fields  PROBAB THEORY RELAT FIELD
, vol. 111, no. 3, pp. 333374, 1998
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Citations
(20)
Effective Pharmacological Management of Gastrointestinal Vascular Lesions With Long Acting Octreotide: A Case Series
Spyros Michopoulos
,
Evanthia Zampeli
,
Charalambos Giannopoulos
,
Michael Mavros
,
Panayiotis Anapliotis
,
Vassilios Xourafas
Journal:
Gastroenterology
, vol. 140, no. 5, pp. S388S388, 2011
On Stratonovich and Skorohod stochastic calculus for Gaussian processes
Samy Tindel
,
Maria Jolis
,
Yaozhong Hu
Published in 2011.
The rough path associated to the multidimensional analytic fBm with any Hurst parameter
Samy Tindel
,
Jérémie Unterberger
Journal:
Collectanea Mathematica  COLLECT MATH
, vol. 62, no. 2, pp. 197223, 2011
A modification for the maskfiltering approach by superposing anisotropic derivatives in an image
ChingChung Yang
Journal:
Optik
, vol. 122, no. 18, pp. 16841687, 2011
Rough path stability of SPDEs arising in nonlinear filtering
(
Citations: 4
)
Peter Friz
,
Harald Oberhauser
Published in 2010.