Intermittence and nonlinear parabolic stochastic partial differential equations.
Linear expansion of isotropic Brownian flows.
Local and global existence for mild solutions of stochastic differential equations.
Malliavin calculus for two-parameter processes
Malliavin method for optimal investment in financial markets with memory
We consider a financial market with memory effects in which wealth processes are driven by mean-field stochastic Volterra equations. In this financial market, the classical dynamic programming method can not be used to study the optimal investment problem, because the solution of mean-field stochastic Volterra equation is not a Markov process. In this paper, a new method through Malliavin calculus introduced in [1], can be used to obtain the optimal investment in a Volterra type financial market....
Markov operators defined by Volterra type integrals with advanced argument
Martingales on noncompact manifolds : maximal inequalities and prescribed limits
Mild solutions of quantum stochastic differential equations.
Minimal supersolutions of BSDEs with lower semicontinuous generators
We study minimal supersolutions of backward stochastic differential equations. We show the existence and uniqueness of the minimal supersolution, if the generator is jointly lower semicontinuous, bounded from below by an affine function of the control variable, and satisfies a specific normalization property. Semimartingale convergence is used to establish the main result.
Nonlinear evolution equations on Banach space.
Nonlinear stochastic functional integral equations in the plane.
Note on a stochastic integral equation
Numerical simulations for stochastic lattice equations.
On a class of stochastic functional integral equations
On a pair of random generalized non-linear contractions.
On existence and an asymptotic behavior of random solutions of a class of stochastic functional-integral equations
On existence, uniqueness and stability of solutions of multidimensional SDE's with reflecting boundary conditions
On filtering over Îto-Volterra observations.
On Fredholm integral equations with random degenerate kernels
On one-dimensional diffusion processes living in a bounded space interval
We prove that under some assumptions a one-dimensional Itô equation has a strong solution concentrated on a finite spatial interval, and the pathwise uniqueness holds.