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 for observations on a random vector field along a random path. Application to atmospheric turbulent velocities
To filter perturbed local measurements on a random medium, a dynamic model jointly with an observation transfer equation are needed. Some media given by PDE could have a local probabilistic representation by a Lagrangian stochastic process with mean-field interactions. In this case, we define the acquisition process of locally homogeneous medium along a random path by a Lagrangian Markov process conditioned to be in a domain following the path and conditioned to the observations. The nonlinear...
Nonlinear filtering for reflecting diffusions in random environments via nonparametric estimation.
Nonlinear filtering in spatio–temporal doubly stochastic point processes driven by OU processes
Doubly stochastic point processes driven by non-Gaussian Ornstein–Uhlenbeck type processes are studied. The problem of nonlinear filtering is investigated. For temporal point processes the characteristic form for the differential generator of the driving process is used to obtain a stochastic differential equation for the conditional distribution. The main result in the spatio-temporal case leads to the filtering equation for the conditional mean.
Nonlinear filtering with an infinite dimensional signal process.
Nonlinear filtering with signal dependent observation noise.
Nonlinear Markov processes in big networks
Big networks express multiple classes of large-scale networks in many practical areas such as computer networks, internet of things, cloud computation, manufacturing systems, transportation networks, and healthcare systems. This paper analyzes such big networks, and applies the mean-field theory and the nonlinear Markov processes to constructing a broad class of nonlinear continuous-time block-structured Markov processes, which can be used to deal with many practical stochastic systems. Firstly,...
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 .
Nonlinear stochastic homogenization and ergodic theory.
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.
Nonlinear structures determined by measures on Banach spaces
Non-linear Wiener-Hopf theory, 1 : an appetizer
Nonmonotonic coexistence regions for the two-type Richardson model on graphs.
Non-negative linear processes
Conditions under which the linear process is non-negative are investigated in the paper. In the definition of the linear process a strict white noise is used. Explicit results are presented also for the models AR(1) and AR(2).