FRACTIONAL BROWNIAN MOTION AND STOCHASTIC EQUATIONS IN HILBERT SPACES

By Tyrone E. Duncan, Bozenna Pasik-Duncan, Bohdan Maslowski. 2002

185 citations recorded by the source corpus.

Subfields: Applied Mathematics, Finance

View Paper: https://www.semanticscholar.org/paper/ef97f9f096d2b227869a0812b3199fc7326e551e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. David Nualart
2. Massimiliano Gubinelli
3. Samy Tindel
4. Yaozhong Hu
5. Ciprian A. Tudor
6. Antoine Lejay
7. Kexue Li
8. Peter K. Friz

In Finance

1. David Nualart
2. Samy Tindel
3. Yaozhong Hu
4. Ciprian A. Tudor
5. Massimiliano Gubinelli
6. Antoine Lejay
7. Frederi G. Viens
8. R. Balan

Citations in the corpus

• Stochastic evolution equations with fractional Brownian motion (2003, unknown): “AMS Mathematics Subject Classification: 60H15, 60G15, 35G10, 60G17”
• Young Integrals and SPDEs (2004, background): “• In case of a linear equation with additive noise, some optimal conditions on the space covariance of the noise, ensuring the existence and uniqueness of a function-valued solution to the evolution equation, are given in [15], after the pioneering works [6] and [3].”
• Stochastic Heat Equation with Multiplicative Fractional-Colored Noise (2008, background): “What happens when the space-time white noise is replaced by a noise which is fractional in time, but continues to be white in space? This situation has been studied in several papers such as [14], [24], [29], [34] and recently in [1].”
• Variational solutions for partial differential equations driven by a fractional noise (2006, background): “…by a multiplicative, multiparameter fractional noise and estimated the Lyapunov exponents of the corresponding solutions; finally, the authors of [18] and [38] have proved the existence and the uniqueness of mild solutions to various classes of stochastic evolution equations driven by a…”
• Stochastic heat equation driven by fractional noise and local time (2007, background): “in [3] in the case H ∈ (12 , 1) and by Tindel et al.”
• Stochastic delay fractional evolution equations driven by fractional Brownian motion (2014, background): “[11] studied stochastic differential equations driven by cylindrical fractional Brownian motion with Hurst parameter H ∈ ((1) 2 , 1).”
• Local times of fractional Brownian sheets (2002, unknown): “Stochastic partial differential equations driven by fractional Brownian sheet have been studied by Øksendal and Zhang (2000), Hu, Øksendal and Zhang (2000) and Duncan et al. (2000).”