Approximation by time discretization of special stochastic evolution equations.
Approximation of attractors for multivalued random dynamical systems
Approximation of stochastic advection diffusion equations with stochastic alternating direction explicit methods
The numerical solutions of stochastic partial differential equations of Itô type with time white noise process, using stable stochastic explicit finite difference methods are considered in the paper. Basically, Stochastic Alternating Direction Explicit (SADE) finite difference schemes for solving stochastic time dependent advection-diffusion and diffusion equations are represented and the main properties of these stochastic numerical methods, e.g. stability, consistency and convergence are analyzed....
Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions [Book]
Approximations to mild solutions of stochastic semilinear equations.
Approximations to mild solutions of stochastic semilinear equations with non-Lipschitz coefficients
In the present paper, using a Picard type method of approximation, we investigate the global existence of mild solutions for a class of Ito type stochastic differential equations whose coefficients satisfy conditions more general than the Lipschitz and linear growth ones.
Asymptotic Properties of Stochastic Semilinear Equations by the Method of Lower Measures
Asymptotic solutions of diffusion models for risk reserves.
Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations
This work is concerned with the asymptotic analysis of a time-splitting scheme for the Schrödinger equation with a random potential having weak amplitude, fast oscillations in time and space, and long-range correlations. Such a problem arises for instance in the simulation of waves propagating in random media in the paraxial approximation. The high-frequency limit of the Schrödinger equation leads to different regimes depending on the distance of propagation, the oscillation pattern of the initial...
Attractors for stochastic reaction-diffusion equation with additive homogeneous noise
We study the asymptotic behaviour of solutions of a reaction-diffusion equation in the whole space driven by a spatially homogeneous Wiener process with finite spectral measure. The existence of a random attractor is established for initial data in suitable weighted -space in any dimension, which complements the result from P. W. Bates, K. Lu, and B. Wang (2013). Asymptotic compactness is obtained using elements of the method of short trajectories.
Axial shear modulus of a fiber-reinforced composite with random fiber cross-sections.
Bounded and periodic solutions of the Riccati equation in Banach space.
Brownian representations of cylindrical local martingales, martingale problem and strong Markov property of weak solutions of SPDEs in Banach spaces
The paper deals with three issues. First we show a sufficient condition for a cylindrical local martingale to be a stochastic integral with respect to a cylindrical Wiener process. Secondly, we state an infinite dimensional version of the martingale problem of Stroock and Varadhan, and finally we apply the results to show that a weak existence plus uniqueness in law for deterministic initial conditions for an abstract stochastic evolution equation in a Banach space implies the strong Markov property....
BSDE associated with Lévy processes and application to PDIE.
Calcul stochastique non commutatif
Cálculo diferencial estocástico para procesos con parámetro n-dimensional.
In this paper we obtain a representation of semimartingalas in the plane by means of stochastic integrals. Some applications to the study of random Markov gaussian fields are given.
Characterization of the domain of an elliptic operator of infinitely many variables in spaces
We consider an elliptic operator associated to a Dirichlet form corresponding to a differential stochastic equation of potential form. We characterize the domain of the operator as a subspace of , where is the invariant measure of the differential stochastic equation.
Comparison principle approach to utility maximization
We consider the problem of optimal investment for maximal expected utility in an incomplete market with trading strategies subject to closed constraints. Under the assumption that the underlying utility function has constant sign, we employ the comparison principle for BSDEs to construct a family of supermartingales leading to a necessary and sufficient condition for optimality. As a consequence, the value function is characterized as the initial value of a BSDE with Lipschitz growth.
Comportement des fonctions biharmoniques là où l'intégrale d'aire est finie
Condiciones suficientes de estabilidad para ecuaciones en derivadas parciales estocásticas con retardos.