Stochastic Heat Equation with Multiplicative Fractional-Colored Noise
نویسندگان
چکیده
منابع مشابه
Stochastic Heat Equation with Multiplicative Fractional-Colored Noise
We consider the stochastic heat equation with multiplicative noise ut = 1 2 ∆u + uẆ in R+ × R , whose solution is interpreted in the mild sense. The noise Ẇ is fractional in time (with Hurst index H ≥ 1/2), and colored in space (with spatial covariance kernel f). When H > 1/2, the equation generalizes the Itô-sense equation for H = 1/2. We prove that if f is the Riesz kernel of order α, or the ...
متن کاملThe Stochastic Heat Equation with a Fractional-colored Noise: Existence of the Solution
Abstract. In this article we consider the stochastic heat equation ut −∆u = Ḃ in (0, T )× R, with vanishing initial conditions, driven by a Gaussian noise Ḃ which is fractional in time, with Hurst index H ∈ (1/2, 1), and colored in space, with spatial covariance given by a function f . Our main result gives the necessary and sufficient condition on H for the existence of the process solution. W...
متن کاملThe Stochastic Heat Equation with Fractional-Colored Noise: Existence of the Solution
Abstract. In this article we consider the stochastic heat equation ut −∆u = Ḃ in (0, T )×Rd, with vanishing initial conditions, driven by a Gaussian noise Ḃ which is fractional in time, with Hurst index H ∈ (1/2, 1), and colored in space, with spatial covariance given by a function f . Our main result gives the necessary and sufficient condition on H for the existence of a solution. When f is t...
متن کاملQuadratic variations for the fractional-colored stochastic heat equation∗
Using multiple stochastic integrals and Malliavin calculus, we analyze the quadratic variations of a class of Gaussian processes that contains the linear stochastic heat equation on R driven by a non-white noise which is fractional Gaussian with respect to the time variable (Hurst parameter H) and has colored spatial covariance of α-Riesz-kernel type. The processes in this class are self-simila...
متن کاملStochastic Heat Equation with Infinite Dimensional Fractional Noise: L2-theory
In this article we consider the stochastic heat equation in [0, T ]× Rd, driven by a sequence (β)k of i.i.d. fractional Brownian motions of index H > 1/2 and random multiplication functions (g)k. The stochastic integrals are of Hitsuda-Skorohod type and the solution is interpreted in the weak sense. Using Malliavin calculus techniques, we prove the existence and uniqueness of the solution in a ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Theoretical Probability
سال: 2009
ISSN: 0894-9840,1572-9230
DOI: 10.1007/s10959-009-0237-3