相关论文: A min-type stochastic fixed-point equation related…

We study the asymptotic behavior of mixed functionals of the form $I_T(t)=F_T(\xi_T(t))+\int_0^tg_T(\xi_T(s))\,d\xi_T(s)$, $t\ge0$, as $T\to\infty$. Here $\xi_T(t)$ is a strong solution of the stochastic differential equation…

We establish regularity and, under suitable assumptions, convergence to stationary states for weak solutions of a parabolic equation with a non-linear non-local drift term; this equation was derived from a model of active Brownian particles…

In this paper we study the Stratonovich stochastic differential equation $\mathrm{d} X=|X|^{\alpha}\circ\mathrm{d} B$, $\alpha\in(-1,1)$, which has been introduced by Cherstvy et al. [New Journal of Physics 15:083039 (2013)] in the context…

We consider the rate of piecewise constant approximation to a locally stationary process $X(t),t\in [0,1]$, having a variable smoothness index $\alpha(t)$. Assuming that $\alpha(\cdot)$ attains its unique minimum at zero and satisfies the…

One proves the $H$-theorem for mild solutions to a nondegenerate, nonlinear Fokker-Planck equation $$ u_t-\Delta\beta(u)+{\rm div}(D(x)b(u)u)=0, \ t\geq0, \ x\in\mathbb{R}^d,\qquad (1)$$ and under appropriate hypotheses on $\beta,$ $D$ and…

Convection-diffusion equations arise in a variety of applications such as particle transport, electromagnetics, and magnetohydrodynamics. Simulation of the convection-dominated regime for these problems, even with high-fidelity techniques,…

This paper is concerned with the following Markovian stochastic differential equation of mean-reversion type \[ dR_t= (\theta +\sigma \alpha(R_t, t))R_t dt +\sigma R_t dB_t \] with an initial value $R_0=r_0\in\mathbb{R}$, where…

Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori…

We construct non-negative martingale solutions to the stochastic porous medium equation in one dimension with homogeneous Dirichlet boundary conditions which exhibit a type of sticky behavior at zero. The construction uses the stochastic…

The main result of the present paper is a statement on existence, uniqueness and regularity for mild solutions to a parabolic transport diffusion type equation that involves a non-smooth coefficient. We investigate related Cauchy problems…

The well-known Edwards-Wilkinson equation with a flow term added exhibits a smoothing fixed point in addition to the normal EW fixed point. Based on this, we present a model of sandpiles involving a coupling between fixed and mobile grains,…

Motivated by the work of T.E. Govindan in [5,8,9], this paper is concerned with a more general semilinear stochastic evolution equation. The difference between the equations considered in this paper and the previous one is that it makes…

We consider solutions to so-called stochastic fixed point equation $R \stackrel{d}{=} \Psi(R)$, where $\Psi $ is a random Lipschitz function and $R$ is a random variable independent of $\Psi$. Under the assumption that $\Psi$ can be…

We show a stochastic version of the Schauder-Tychonoff fixed point theorem which yields a solution of the martingale problem for a class of systems of nonlinear reaction-diffusion equations driven by a cylindrical Wiener process and a…

We extend the convergence analysis of the Scholtes-type regularization method for cardinality-constrained optimization problems. Its behavior is clarified in the vicinity of saddle points, and not just of minimizers as it has been done in…

This paper considers approximate smoothing for discretely observed non-linear stochastic differential equations. The problem is tackled by developing methods for linearising stochastic differential equations with respect to an arbitrary…

In this paper, we study the existence of solutions to sweeping processes in the presence of stochastic perturbations, where the moving set takes uniformly prox-regular values and varies continuously with respect to the Hausdorff distance,…

We study stochastic differential equations on the $d$-dimensional flat torus $\mathbb{T}^d$ with drift and perturbation coefficients in $L^{\infty}(\mathbb{T}^d;\mathbb{R}^d)$ and additive non-degenerate noise. For the associated transfer…

We study triangulation schemes for the joint kernel of a diffusion process with uniformly continuous coefficients and an adapted, non-resonant Abelian process. The prototypical example of Abelian process to which our methods apply is given…

In a separable Hilbert space, we study the minimization problem of a convex smooth function with Lipschitz continuous gradient whose evaluations are corrupted by random noise. To this end, we associate a stochastic inertial system that…