Related papers: Matrix-noise Jacobians in stochastic-calculus infe…
We consider a nonlinear stochastic partial differential equation (SPDE) that takes the form of the Camassa--Holm equation perturbed by a convective, position-dependent, noise term. We establish the first global-in-time existence result for…
We prove the existence of multiple noise-induced transitions in the Lasota-Mackey map, which is a class of one dimensional random dynamical system with additive noise. The result is achieved by the help of rigorous computer assisted…
In the "stochastic $\delta N$ formalism", the statistics of the inflationary density perturbation are obtained from the first passage distribution of a stochastic process. We develop a general framework in which to evaluate the rare tail of…
We observe a $N\times M$ matrix $Y_{ij}=s_{ij}+\xi_{ij}$ with $\xi_{ij}\sim {\mathcal {N}}(0,1)$ i.i.d. in $i,j$, and $s_{ij}\in \mathbb {R}$. We test the null hypothesis $s_{ij}=0$ for all $i,j$ against the alternative that there exists…
This work concerns the minimization of the pseudospectral abscissa of a matrix-valued function dependent on parameters analytically. The problem is motivated by robust stability and transient behavior considerations for a linear control…
The fully discrete problem for convection-diffusion equation is considered. It comprises compact approximations for spatial discretization, and Crank-Nicolson scheme for temporal discretization. The expressions for the entries of inverse of…
We study a semismooth Newton-type method for the nearest doubly stochastic matrix problem where both differentiability and nonsingularity of the Jacobian can fail. The optimality conditions for this problem are formulated as a system of…
We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
The path probability of stochastic motion of non dissipative or quasi-Hamiltonian systems is investigated by numerical experiment. The simulation model generates ideal one-dimensional motion of particles subject only to conservative forces…
We study the noise-induced escape from a stable limit cycle of a non-gradient dynamical system driven by a small additive noise. The fact that the optimal transition path in this case is infinitely long imposes a severe numerical challenge…
Over the last 50 years a steady stream of accounts have been written on the separation principle of stochastic control. Even in the context of the linear-quadratic regulator in continuous time with Gaussian white noise, subtle difficulties…
We provide a simple framework for the study of parametric (multiplicative) noise, making use of scale parameters. We show that for a large class of stochastic differential equations increasing the multiplicative noise intensity surprisingly…
A large deviation principle is established for a two-scale stochastic system in which the slow component is a continuous process given by a small noise finite dimensional It\^{o} stochastic differential equation, and the fast component is a…
Bistable autonomous systems can be found inmany areas of science. When the intrinsic noise intensity is large, these systems exhibits stochastic transitions from onemetastable steady state to another. In electronic bistable memories, these…
We study the homogenization of nonlinear, first-order equations with highly oscillatory mixing spatio-temporal dependence. It is shown in a variety of settings that the homogenized equations are stochastic Hamilton-Jacobi equations with…
The influence of multiplicative stochastic perturbations on the class of asymptotically Hamiltonian systems on the plane is investigated. It is assumed that disturbances do not preserve the equilibrium of the corresponding limiting system…
We consider multistage stochastic linear optimization problems combining joint dynamic probabilistic constraints with hard constraints. We develop a method for projecting decision rules onto hard constraints of wait-and-see type. We…
A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in space and a stochastic trigonometric method for the temporal…
Continuous-discrete models with dynamics described by stochastic differential equations are used in a wide variety of applications. For these systems, the maximum a posteriori (MAP) state path can be defined as the curves around which lie…