Existence and uniqueness of solutions to a class of stochastic functional partial differential equations via integral contractors.
Existence and uniqueness to the Cauchy problem for linear and semilinear parabolic equations with local conditions⋆
We consider the Cauchy problem in ℝd for a class of semilinear parabolic partial differential equations that arises in some stochastic control problems. We assume that the coefficients are unbounded and locally Lipschitz, not necessarily differentiable, with continuous data and local uniform ellipticity. We construct a classical solution by approximation with linear parabolic equations. The linear equations involved can not be solved with the traditional...
Existence of density for the solution to the three-dimensional wave equation.
We prove existence of density for the real-valued solution to a 3-dimensional stochastic wave equation (...).
Existence of explosive solutions to some nonlinear parabolic Itô equations
The paper is concerned with the problem of existence of explosive solutions for a class of nonlinear parabolic Itô equations. Under some sufficient conditions on the initial state and the coefficients, it is proven by the method of auxiliary functionals that there exist explosive solutions with positive probability. The main results are presented in Theorems 3.1 and 3.2 under different sets of conditions. An example is given to illustrate some application of the second theorem.
Existence of quadratic-mean almost periodic solutions to some stochastic hyperbolic differential equations.
Existence, uniqueness and ergodicity for the stochastic quantization equation
Existence, uniqueness and ergodicity of weak solutions to the equation of stochastic quantization in finite volume is obtained as a simple consequence of the Girsanov theorem.
Existence, uniqueness and regularity of parabolic SPDEs driven by Poisson random measure.
Existence, uniqueness and statistical theory of turbulent solutions of the stochastic Navier-Stokes equation, in three dimensions -- an overview.
Explosion en temps fini pour l’équation de Schrödinger non linéaire stochastique surcritique
Exponential convergence for a periodically driven semilinear heat equation
Exponential ergodicity of semilinear equations driven by Lévy processes in Hilbert spaces
We study convergence to the invariant measure for a class of semilinear stochastic evolution equations driven by Lévy noise, including the case of cylindrical noise. For a certain class of equations we prove the exponential rate of convergence in the norm of total variation. Our general result is applied to a number of specific equations driven by cylindrical symmetric α-stable noise and/or cylindrical Wiener noise. We also consider the case of a "singular" Wiener process with unbounded covariance...
Extending martingale measure stochastic integral with applications to spatially homogeneous S. P. D. E's.
Extinction for two parabolic stochastic PDE's on the lattice