A note on Krylov's -theory for systems of SPDEs.
A note on large deviations for Wiener chaos
A note on maximal estimates for stochastic convolutions
In stochastic partial differential equations it is important to have pathwise regularity properties of stochastic convolutions. In this note we present a new sufficient condition for the pathwise continuity of stochastic convolutions in Banach spaces.
A note on maximal inequality for stochastic convolutions
Using unitary dilations we give a very simple proof of the maximal inequality for a stochastic convolution driven by a Wiener process in a Hilbert space in the case when the semigroup is of contraction type.
A note on one-dimensional stochastic equations
We consider the stochastic equation where is a one-dimensional Brownian motion, is the initial value, and is a time-dependent diffusion coefficient. While the existence of solutions is well-studied for only measurable diffusion coefficients , beyond the homogeneous case there is no general result on the uniqueness in law of the solution. The purpose of the present note is to give conditions on ensuring the existence as well as the uniqueness in law of the solution.
A note on parabolic convexity and heat conduction
A note on stochastic integration with respect to optional semimartingales.
A note on -stochastic operators
A note on strong solutions of stochastic differential equations with a discontinuous drift coefficient.
A note on the functional law of the iterated logarithm for Lévy's area process
By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in Hölder norm, for Lévy's area process.
A note on the Runge-Kutta method for stochastic differential equations
In the paper the convergence of a mixed Runge--Kutta method of the first and second orders to a strong solution of the Ito stochastic differential equation is studied under a monotonicity condition.
A note on weak solutions to stochastic differential equations
We revisit the proof of existence of weak solutions of stochastic differential equations with continuous coeficients. In standard proofs, the coefficients are approximated by more regular ones and it is necessary to prove that: i) the laws of solutions of approximating equations form a tight set of measures on the paths space, ii) its cluster points are laws of solutions of the limit equation. We aim at showing that both steps may be done in a particularly simple and elementary manner.
A note on γ-radonifying and summing operators
In this note, we discuss certain generalizations of γ-radonifying operators and their applications to the regularity for linear stochastic evolution equations on some special Banach spaces. Furthermore, we also consider a more general class of operators, namely the so-called summing operators and discuss the application to the compactness of the heat semi-group between weighted -spaces.
A note to paper “On the stability of cubic mappings and quartic mappings in random normed spaces”.
A pathwise solution for nonlinear parabolic equations with stochastic perturbations
We analyse here a semilinear stochastic partial differential equation of parabolic type where the diffusion vector fields are depending on both the unknown function and its gradient ∂ xu with respect to the state variable, ∈ ℝn. A local solution is constructed by reducing the original equation to a nonlinear parabolic one without stochastic perturbations and it is based on a finite dimensional Lie algebra generated by the given diffusion vector fields.
A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities
A post-predictive view of gaussian processes
A probabilistic approach to the boundedness of singular integral operators
A probabilistic representation for the solutions to some non-linear PDEs using pruned branching trees
A proof of admissibility of a class of random normed spaces