Related papers: Representation for filtration-consistent nonlinear…
This paper explores a class of fully coupled nonlinear forward-backward stochastic difference equations (FBS$\Delta$Es). Building on insights from linear quadratic optimal control problems, we introduce a more relaxed framework of…
We consider a rather general class of evolutionary PDEs involving dissipation (of possibly fractional order), which competes with quadratic nonlinearities on the regularity of the overall equation. This includes as prototype models,…
This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…
Let $G$ be a finite group of Lie type and $\ell$ be a prime which is not equal to the defining characteristic of $G$. In this note we discuss some open problems concerning the $\ell$-modular irreducible representations of $G$. We also…
In this article, using DiPerna-Lions theory \cite{Di-Li}, we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and…
This paper is devoted to proving a general invariant representation theorem for generators of general time interval backward stochastic differential equations, where the generator $g$ has a quadratic growth in the unknown variable $z$ and…
We provides some useful estimates for solving martingale representation problem under G-expectations. We also study the corresponding conditions for the existence and uniqueness.
We consider a system of semilinear partial differential equations (PDEs) with a nonlinearity depending on both the solution and its gradient. The Neumann boundary condition depends on the solution in a nonlinear manner. The uniform…
The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven. This type of stochastic PDE is shown to arise in the mean field limit of weakly interacting diffusions with…
In this article we study perturbations of local, nonlinear Dirichlet forms on arbitrary topological measure spaces. We show that the semigroup of a local Dirichlet form \(\mathcal{E}\) dominates the semigroup generated by another functional…
We analyse the underlying nonlinear partial differential equation which arises in the study of gravitating flat fluid plates of embedding class one. Our interest in this equation lies in discussing new solutions that can be found by means…
The Gaussian Filter (GF) is one of the most widely used filtering algorithms; instances are the Extended Kalman Filter, the Unscented Kalman Filter and the Divided Difference Filter. GFs represent the belief of the current state by a…
Modern analyses of diffusion processes have proposed nonlinear versions of the Fokker-Planck equation to account for non-classical diffusion. These nonlinear equations are usually constructed on a phenomenological basis. Here we introduce a…
In this paper, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, we provide a framework from which we can provide conditions, which are straightforward to check, for the solvability…
We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…
In this paper we provide a new (probabilistic) proof of a classical result in partial differential equations, viz. if $\phi$ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition…
A qualitative representation $\phi$ is like an ordinary representation of a relation algebra, but instead of requiring $(a; b)^\phi = a^\phi | b^\phi$, as we do for ordinary representations, we only require that $c^\phi\supseteq a^\phi |…
Given a real valued and time-inhomogeneous martingale diffusion X, we investigate the properties of functions defined by the conditional expectation f(t,X_t)=E[g(X_T)|F_t]. We show that whenever g is monotonic or Lipschitz continuous then…
In this paper, we establish blow-up results for the semilinear wave equation in generalized Einstein-de Sitter spacetime with nonlinearity of derivative type. Our approach is based on the integral representation formula for the solution to…
A general approach is presented to describing nonlinear classical Maxwell electrodynamics with conformal symmetry. We introduce generalized nonlinear constitutive equations, expressed in terms of constitutive tensors dependent on…