Nonlinear elliptic systems in stochastic game theory.
Nonlinear evolution equations on Banach space.
Nonlinear filtering for Markov systems with delayed observations
This paper deals with nonlinear filtering problems with delays, i.e., we consider a system (X,Y), which can be represented by means of a system (X,Ŷ), in the sense that Yt = Ŷa(t), where a(t) is a delayed time transformation. We start with X being a Markov process, and then study Markovian systems, not necessarily diffusive, with correlated noises. The interest is focused on the existence of explicit representations of the corresponding filters as functionals depending on the observed trajectory....
Nonlinear filtering with an infinite dimensional signal process.
Non-linear Neumann's condition for the heat equation : a probabilistic representation using catalytic super-brownian motion
Nonlinear parabolic SPDEs involving Dirichlet operators
We study the problem of existence, uniqueness and regularity of probabilistic solutions of the Cauchy problem for nonlinear stochastic partial differential equations involving operators corresponding to regular (nonsymmetric) Dirichlet forms. In the proofs we combine the methods of backward doubly stochastic differential equations with those of probabilistic potential theory and Dirichlet forms.
Nonlinear Random Equations with Monotone Operators in Banach Spaces.
Nonlinear state prediction by separation approach for continuous-discrete stochastic systems
The paper deals with a filter design for nonlinear continuous stochastic systems with discrete-time measurements. The general recursive solution is given by the Fokker–Planck equation (FPE) and by the Bayesian rule. The stress is laid on the computation of the predictive conditional probability density function from the FPE. The solution of the FPE and its integration into the estimation algorithm is the cornerstone for the whole recursive computation. A new usable numerical scheme for the FPE is...
Nonlinear stochastic functional integral equations in the plane.
Nonlinear stochastic heat equations with cubic nonlinearities and additive -regular noise in .
Non-linear stochastic partial differential equations with delays: existence and uniqueness of solutions.
The main aim of this paper is to study stochastic PDE's with delay terms. In fact, we prove existence and uniqueness of solutions (in Itô's sense) for a rather general type of stochastic PDE's with non-linear monotone operators and with delays.
Nonstandard methods for Navier-Stokes equations
Non-symmetric approximations for manifold-valued semimartingales
Non-symmetric hitting distributions on the hyperbolic half-plane and subordinated perpetuities.
We study the law of functionals whose prototype is ∫0+∞ eBs(ν) dWs(μ),where B(ν) and W(μ) are independent Brownian motions with drift. These functionals appear naturally in risk theory as well as in the study of in variant diffusions on the hyperbolic half-plane. Emphasis is put on the fact that the results are obtained in two independent, very different fashions (invariant diffusions on the hyperbolic half-plane and Bessel processes).
Normal martingales and polynomial families
Wiener and compensated Poisson processes, as normal martingales, are associated to classical sequences of polynomials, namely Hermite polynomials for the first one and Charlier polynomials for the second. The problem studied in this paper is to find if there exist other normal martingales which are associated to classical sequences of polynomials. Privault, Solé and Vives [5] solved this problem via the quantum Kabanov formula under some assumptions on the normal martingales considered. We solve...
Normalized stochastic integrals in topological vector spaces
Note on a stochastic integral equation
Note on the internal stabilization of stochastic parabolic equations with linearly multiplicative gaussian noise
The parabolic equations driven by linearly multiplicative Gaussian noise are stabilizable in probability by linear feedback controllers with support in a suitably chosen open subset of the domain. This procedure extends to Navier − Stokes equations with multiplicative noise. The exact controllability is also discussed.
Note on the selection properties of set-valued semimartingales
Set-valued semimartingales are introduced as an extension of the notion of single-valued semimartingales. For such multivalued processes their semimartingale selection properties are investigated.
Note sur les processus d'Ornstein-Uhlenbeck