Related papers: Errata to Stochastic explosion and non-uniqueness …
In this paper, we study linear-quadratic control problems for stochastic Volterra integral equations with singular and non-convolution-type coefficients. The weighting matrices in the cost functional are not assumed to be non-negative…
We propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear…
The problem of linearization by point transformations is solved for equations in the generalized Riccati and Abel chain of order not exceeding the fourth. It is shown in particular that nonlinear third order and fourth order equations from…
We study a nonlinear and nonlocal elliptic equation posed on the flat torus. While constant solutions always exist, we show that uniqueness fails in general. Using spectral analysis and the Crandall--Rabinowitz bifurcation theorem, we prove…
A novel recipe for exactly solving in finite terms a class of special differential Riccati equations is reported. Our procedure is entirely based on a successful resolution strategy quite recently applied to quantum dynamical time-dependent…
It is a longstanding unsolved problem to characterize the optimal feedback controls for general linear quadratic optimal control problem of stochastic evolution equation with random coefficients. A solution to this problem is given in [21]…
A Comment by R. Blumenfeld on our recent analytical solution for the random close packing density [A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)] is shown to be plagued by important errors and to contain incorrect statements.
This paper is concerned with a type of nonlinear reaction-diffusion equation, which arises from the population dynamics. The equation includes a certain type reaction term $u^\alpha(1- \sigma \int_{\R^n}u^\beta dx)$ of dimension $n \ge 1$…
The uniqueness argument in the proof of Theorem 5, p. 483, of "Small noise asymptotics for invariant densities for a class of diffusions: a control theoretic view, J. Math. Anal. and Appl. (2009) " is flawed. We give here a corrected proof.
This paper has being withdrawn by the authors due to an error in the conclusion.
This is an erratum to 'On the quantitative distribution of polynomial nilsequences' [GT]. The proof of Theorem 8.6 of that paper, which claims a distribution result for multiparameter polynomial sequences on nilmanifolds, was incorrect. We…
This paper has been withdrawn by the author, due to a crucial error in page 5.
In this note, we prove the uniqueness of blowups at singular points of the no-sign obstacle problem $\Delta u=\chi_{_{B_1\backslash \{u=|Du|=0\}}}\ \text{in}\ B_1,$ thus give a positive answer to a problem raised in \cite[Notes of Chaper 7,…
In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional…
In this paper we will develop linear and nonlinear filtering methods for a large class of nonlinear wave equations that arise in applications such as quantum dynamics and laser generation and propagation in a unified framework. We consider…
This paper is withdrawn by the author due to a critical error in the proof of the main theorem, Theorem 3.10. (More specifically the identity (5.18) is incorrect in that the $T^*S^1(2)$-factor is missing in the right hand side of the…
We establish the uniqueness of the positive solution for equations of the form $-\Delta u=au-b(x)f(u)$ in $\Omega$, $u|\_{\partial\Omega}=\infty$. The special feature is to consider nonlinearities $f$ whose variation at infinity is…
After the publication of [Compos. Math. 156 (2020), no. 4, 822-861], Andrew Putman pointed out a mistake in our paper and helped us fix it. In this note, we will explain what this mistake is and how to fix it.
We study a linear quadratic optimal control problem with stochastic coefficients and a terminal state constraint, which may be in force merely on a set with positive, but not necessarily full probability. Under such a partial terminal…
I show that the main statement of [Phys. Rev. Lett. 105, 094802 (2010), arXiv:1005.2617] is wrong. Other inconsistences of this Letter are also discussed.