216 research outputs found
Large deviations for invariant measures of SPDEs with two reflecting walls
In this article, we established a large deviation principle for invariant
measures of solutions of stochastic partial differential equations with two
reflecting walls driven by space-time white noise
A probabilistic approach to Dirichlet problems of semilinear elliptic PDEs with singular coefficients
In this paper, we prove that there exists a unique solution to the Dirichlet
boundary value problem for a general class of semilinear second order elliptic
partial differential equations. Our approach is probabilistic. The theory of
Dirichlet processes and backward stochastic differential equations play a
crucial role.Comment: Published in at http://dx.doi.org/10.1214/10-AOP591 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Lattice Approximations of Reflected Stochastic Partial Differential Equations Driven by Space-Time White Noise
We introduce a discretization/approximation scheme for reflected stochastic
partial differential equations driven by space-time white noise through systems
of reflecting stochastic differential equations. To establish the convergence
of the scheme, we study the existence and uniqueness of solutions of
Skorohod-type deterministic systems on time-dependent domains. We also need to
establish the convergence of an approximation scheme for deterministic
parabolic obstacle problems. Both are of independent interest on their own
Stochastic differential equations with non-lipschitz coefficients: I. Pathwise uniqueness and large deviation
We study a class of stochastic differential equations with non-Lipschitzian
coefficients.A unique strong solution is obtained and a large deviation
principle of Freidln-Wentzell type has been established.Comment: A short version will be published in C. R. Acad. Pari
Quasilinear parabolic stochastic partial differential equations: existence, uniqueness
In this paper, we provide a direct approach to the existence and uniqueness
of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to
quasilinear stochastic partial differential equations, which are neither
monotone nor locally monotone
Stochastic differential equtions with non-lipschitz coefficients:II. Dependence with respect to initial values
The existence of the unique strong solution for a class of stochastic
differential equations with non-Lipschitz coefficients was established
recently. In this paper, we shall investigate the dependence with respect to
the initial values. We shall prove that the non confluence of solutions holds
under our general conditions. To obtain a continuous version, the modulus of
continuity of coefficients is assumed to be less than \dis
|x-y|\log{1\over|x-y|}. In this case, it will give rise to a flow of
homeomorphisms if the coefficients are compactly supported.Comment: 14 page
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