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Ioana Ciotir

Publications and source records attributed to Ioana Ciotir.

23 records · Page 2Linked to original sources
arXiv2013

Probabilistic representation for solutions of a porous media type equation with Neumann boundary condition: the case of the half-line

The purpose of this paper consists in proposing a generalized solution for a porous media type equation on a half-line with Neumann boundary condition and prove a probabilistic representation of this solution in terms of an associated microscopic diffusion. The main idea is to construct a stochastic differential equation with reflection which has a solution in law and whose marginal law densities provide the unique solution of the porous media type equation.

math.PR↗
arXiv2012

Convergence of invariant measures for singular stochastic diffusion equations

It is proved that the solutions to the singular stochastic $p$-Laplace equation, $p\in (1,2)$ and the solutions to the stochastic fast diffusion equation with nonlinearity parameter $r\in (0,1)$ on a bounded open domain $Λ\subset\R^d$ with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters $p$ and $r$ respectively (in the Hilbert spaces $L^2(Λ)$, $H^{-1}(Λ)$ respectively). The highly singular limit case $p=1$ is treated with the help of stochastic evolution variational inequalities, where $\mathbbm{P}$-a.s. convergence, uniformly in time, is established. It is shown that the associated unique invariant measures of the ergodic semigroups converge in the weak sense (of probability measures).

math.PR↗
arXiv2011

Existence and uniqueness of solution for the stochastic nonlinear diffusion equation of plasma

In this paper we are concerned with the stochastic partial differential equations of super-fast diffusion processes describing behavior of plasma dX(t)-Δln(X(t)+1)dt=\surd(Q)dW(t), in (0,T)\timesO, where O is a bounded open subset of R. We define a strong solution adequate to the properties of the natural logarithm and we prove the corresponding existence and uniqueness result.

math.PR↗
arXiv2008

Viability for stochastic differential equations driven by fractional Brownian motion

In this paper we prove a viability result for multidimensional, time dependent, stochastic differential equations driven by fractional Brownian motion with Hurst parameter1/2 < H < 1, using pathwise approach. The sufficient condition is also an alternative global existence result for the fractional differential equations with restrictions on the state.

math.DS↗