On some limit theorems for solutions of stochastic differential equations
On some properties of J-convex stochastic processes.
On some recent aspects of stochastic control and their applications.
On some regularity properties of quadratic stochastic processes.
On some regularity properties of solutions to stochastic evolution equations in Hilbert spaces
On some sample path properties of Skorohod integral processes
On some stability properties of stochastic differential equations of Itô's type
On some stochastic parabolic differential equations in a Hilbert space.
On stability for numerical approximations of stochastic ordinary differential equations.
On stationary distributions for the KPP equation with branching noise
On stochastic differential equations in a configuration space.
On stochastic differential equations with locally unbounded drift
We study the regularizing effect of the noise on differential equations with irregular coefficients. We present existence and uniqueness theorems for stochastic differential equations with locally unbounded drift.
On Stochastic Differential Equations with Reflecting Boundary Condition in Convex Domains
Let D be an open convex set in and let F be a Lipschitz operator defined on the space of adapted càdlàg processes. We show that for any adapted process H and any semimartingale Z there exists a unique strong solution of the following stochastic differential equation (SDE) with reflection on the boundary of D: , t ∈ ℝ⁺. Our proofs are based on new a priori estimates for solutions of the deterministic Skorokhod problem.
On stochastic Euler equation in .
On surrogate learning for linear stability assessment of Navier-Stokes equations with stochastic viscosity
We study linear stability of solutions to the Navier-Stokes equations with stochastic viscosity. Specifically, we assume that the viscosity is given in the form of a stochastic expansion. Stability analysis requires a solution of the steady-state Navier-Stokes equation and then leads to a generalized eigenvalue problem, from which we wish to characterize the real part of the rightmost eigenvalue. While this can be achieved by Monte Carlo simulation, due to its computational cost we study three surrogates...
On the approximate solutions of the Stratonovitch equation.
On the Azéma martingales
On the consistency of a least squares identification procedure
On the constructions of the skew Brownian motion.
On the continuity of random operators.