Stochastic heat equation driven by fractional noise and local time

By Yaozhong Hu, David Nualart. 2007

185 citations recorded by the source corpus.

The aim of this paper is to study the d-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and has the covariance of a fractional Brownian motion with Hurst parameter H ∈ (0,1) in time. Two types of equations are considered. First we consider the equation in the Itô-Skorohod sense, and later in the Stratonovich sense. An explicit chaos expansion for the solution is obtained. On the other hand, the moments of the solution are expressed in terms of the exponential moments of some weighted intersection local time of the Brownian motion.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/de7c763c1fc0e9d7f3ea4f73eefa5c89ce179d71

How researchers see this paper

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

In Finance

1. David Nualart
2. Ciprian A. Tudor
3. Yaozhong Hu
4. Samy Tindel
5. Frederi G. Viens
6. R. Balan
7. Yimin Xiao
8. Yanghui Liu

In Mathematical Physics

1. Ciprian A. Tudor
2. Yaozhong Hu
3. David Nualart
4. R. Balan
5. Yimin Xiao
6. Samy Tindel
7. Jingyu Huang
8. Xia Chen

Citations in the corpus

• Spatial asymptotics for the parabolic Anderson models with generalized time–space Gaussian noise (2016, background): “For the cases labeled (2) in Table 1, it is well known [16] that u(t, x) can be obtained as the L2-limit u(t, x)≡ lim ε→0+ uε(t, x), where uε(t, x) is the solution of (1.”
• Stochastic Heat Equation with Multiplicative Fractional-Colored Noise (2008, methodology): “The correction refers to the fact that the result of [18] is stated incorrectly with the constant σjk = sj ∧ sk + tj ∧ tk, instead of σ∗ jk.”
• Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions (2014, background): “6) for some constant bH,l > 0; the case l= 1 was proved in [16], and the extension to general case is easy; see [9], equation (2.”
• Sample Path Properties of Anisotropic Gaussian Random Fields (2009, background): “differential equations [20; 73; 74; 75]; and in studying the most visited sites of symmetric Markov processes [35].”
• Stochastic heat equations with general multiplicative Gaussian noises: Hölder continuity and intermittency (2014, methodology): “21)), generalize those obtained for the Riesz or the Bessel kernels in [4, 27].”