ترغب بنشر مسار تعليمي؟ اضغط هنا

Quenched asymptotics for a 1-d stochastic heat equation driven by a rough spatial noise

94   0   0.0 ( 0 )
 نشر من قبل Samy Tindel
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise $dot{W}$ in space. We consider the case $H<frac{1}{2}$ and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman-Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form $frac{1}{2} Delta + dot{W}$.



قيم البحث

اقرأ أيضاً

The aim of this paper is to establish the almost sure asymptotic behavior as the space variable becomes large, for the solution to the one spatial dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has th e covariance structure of a fractional Brownian motion with Hurst parameter greater than 1/4 and less than 1/2 in the space variable.
We derive consistent and asymptotically normal estimators for the drift and volatility parameters of the stochastic heat equation driven by an additive space-only white noise when the solution is sampled discretely in the physical domain. We consider both the full space and the bounded domain. We establish the exact spatial regularity of the solution, which in turn, using power-variation arguments, allows building the desired estimators. We show that naive approximations of the derivatives appearing in the power-variation based estimators may create nontrivial biases, which we compute explicitly. The proofs are rooted in Malliavin-Steins method.
This paper studies the nonlinear one-dimensional stochastic heat equation driven by a Gaussian noise which is white in time and which has the covariance of a fractional Brownian motion with Hurst parameter 1/4textless{}Htextless{}1/2 in the space var iable. The existence and uniqueness of the solution u are proved assuming the nonlinear coefficient is differentiable with a Lipschitz derivative and vanishes at 0. In the case of a multiplicative noise, that is the linear equation, we derive the Wiener chaos expansion of the solution and a Feynman-Kac formula for the moments of the solution. These results allow us to establish sharp lower and upper asymptotic bounds for the moments of the solution.
Consider the following stochastic heat equation, begin{align*} frac{partial u_t(x)}{partial t}=- u(-Delta)^{alpha/2} u_t(x)+sigma(u_t(x))dot{F}(t,,x), quad t>0, ; x in R^d. end{align*} Here $- u(-Delta)^{alpha/2}$ is the fractional Laplacian with $ u >0$ and $alpha in (0,2]$, $sigma: Rrightarrow R$ is a globally Lipschitz function, and $dot{F}(t,,x)$ is a Gaussian noise which is white in time and colored in space. Under some suitable additional conditions, we prove a strong comparison theorem and explore the effect of the initial data on the spatial asymptotic properties of the solution. This constitutes an important extension over a series of recent works.
We consider the stochastic heat equation with a multiplicative white noise forcing term under standard intermitency conditions. The main finding of this paper is that, under mild regularity hypotheses, the a.s.-boundedness of the solution $xmapsto u( t,,x)$ can be characterized generically by the decay rate, at $pminfty$, of the initial function $u_0$. More specifically, we prove that there are 3 generic boundedness regimes, depending on the numerical value of $Lambda:= lim_{|x|toinfty} |log u_0(x)|/(log|x|)^{2/3}$.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا