A system of functional-differential equations associated with the optimal detection problem for jump-times of a Poisson process.
A tensor approximation method based on ideal minimal residual formulations for the solution of high-dimensional problems
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal residual method with a measure of the residual corresponding to the error in a specified solution norm. The residual norm can be designed such that the resulting low-rank approximations are optimal with respect to particular norms of interest, thus allowing to take...
A type of Gauss' divergence formula on Wiener spaces.
A unified characterization of -optimal and minimal entropy martingale measures by semimartingale backward equations.
A Weak-Type Inequality for Submartingales and Itô Processes
Let α ∈ [0,1] be a fixed parameter. We show that for any nonnegative submartingale X and any semimartingale Y which is α-subordinate to X, we have the sharp estimate . Here W is the weak- space introduced by Bennett, DeVore and Sharpley. The inequality is already sharp in the context of α-subordinate Itô processes.
A well-posedness result for a mass conserved Allen-Cahn equation with nonlinear diffusion
In this paper, we prove the existence and uniqueness of the solution of the initial boundary value problem for a stochastic mass conserved Allen-Cahn equation with nonlinear diffusion together with a homogeneous Neumann boundary condition in an open bounded domain of with a smooth boundary. We suppose that the additive noise is induced by a Q-Brownian motion.
Absence of absolutely continuous spectrum for some one dimensional random but deterministic Schrödinger operators
Absorption in stochastic epidemics
A two dimensional stochastic differential equation is suggested as a stochastic model for the Kermack–McKendrick epidemics. Its strong (weak) existence and uniqueness and absorption properties are investigated. The examples presented in Section 5 are meant to illustrate possible different asymptotics of a solution to the equation.
Abstract stochastic integro-differential delay equations.
Actions on environment under uncertainty: stochastic formulation and the associated deterministic problem.
Addendum to "Hyperdefinite stochastic integration III".
Adding constraints to BSDEs with jumps: an alternative to multidimensional reflections
This paper is dedicated to the analysis of backward stochastic differential equations (BSDEs) with jumps, subject to an additional global constraint involving all the components of the solution. We study the existence and uniqueness of a minimal solution for these so-called constrained BSDEs with jumps via a penalization procedure. This new type of BSDE offers a nice and practical unifying framework to the notions of constrained BSDEs presented in [S. Peng and M. Xu, Preprint. (2007)] and BSDEs...
Aging for interacting diffusion processes
Algebraic polynomials with random coefficients.
Algèbres de Lie nilpotentes, formule de Baker-Campbell-Hausdorff et intégrales itérées de K.T. Chen
Almost automorphic solution for some stochastic evolution equation driven by Lévy noise with coefficients S2−almost automorphic
In this work we first introduce the concept of Poisson Stepanov-like almost automorphic (Poisson S2−almost automorphic) processes in distribution. We establish some interesting results on the functional space of such processes like an composition theorems. Next, under some suitable assumptions, we establish the existence, the uniqueness and the stability of the square-mean almost automorphic solutions in distribution to a class of abstract stochastic evolution equations driven by Lévy noise in case...
Almost log-optimal trading strategies for small transaction costs in model with stochastic coefficients
We consider a non-consuming agent investing in a stock and a money market interested in the portfolio market price far in the future. We derive a strategy which is almost log-optimal in the long run in the presence of small proportional transaction costs for the case when the rate of return and the volatility of the stock market price are bounded It o processes with bounded coefficients and when the volatility is bounded away from zero.
Almost sure exponential stability of delayed cellular neural networks.
Almost sure exponential stability of neutral differential difference equations with damped stochastic perturbations.
Almost sure properties of controlled diffusions and worst case properties of deterministic systems
We compare a general controlled diffusion process with a deterministic system where a second controller drives the disturbance against the first controller. We show that the two models are equivalent with respect to two properties: the viability (or controlled invariance, or weak invariance) of closed smooth sets, and the existence of a smooth control Lyapunov function ensuring the stabilizability of the system at an equilibrium.