Estimations de grandes déviations pour des systèmes où apparaissent un bruit Gaussien et un bruit non Gaussien
Estudio del carácter markoviano fuerte y regularidades de la solución de ecuaciones integrales estocásticas Ito generalizadas.
El objetivo de este trabajo es un estudio sobre los caracteres felleriano y markoviano fuerte y las propiedades de regularidad del proceso solución de una ecuación integral estocástica generalizada (tipo Ito), pero generalizada en el sentido de considerar una formulación en términos de procesos operador-valuados. Esta formulación generaliza simultánea e independientemente las integrales de Cabaña y Daletsky.
Étude de certains processus (stochastiquement) différentiables ou holomorphes
Étude des opérateurs de Schrödinger à potentiel aléatoire en dimension 1
Étude d'une équation différentielle stochastique avec temps local
Étude d'une fonctionnelle liée au pont de Bessel
Étude probabiliste de l'opérateur de Schrödinger
Euler scheme for SDEs with non-Lipschitz diffusion coefficient : strong convergence
We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form , . In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.
Euler scheme for SDEs with non-Lipschitz diffusion coefficient: strong convergence
We consider one-dimensional stochastic differential equations in the particular case of diffusion coefficient functions of the form |x|α, α ∈ [1/2,1). In that case, we study the rate of convergence of a symmetrized version of the Euler scheme. This symmetrized version is easy to simulate on a computer. We prove its strong convergence and obtain the same rate of convergence as when the coefficients are Lipschitz.
Euler scheme for solutions of stochastic differential equations with non-Lipschitz coefficients.
Euler-Maruyama approximations in mean-reverting stochastic volatility model under regime-switching.
Euler's Approximations of Solutions of Reflecting SDEs with Discontinuous Coefficients
Let D be either a convex domain in or a domain satisfying the conditions (A) and (B) considered by Lions and Sznitman (1984) and Saisho (1987). We investigate convergence in law as well as in for the Euler and Euler-Peano schemes for stochastic differential equations in D with normal reflection at the boundary. The coefficients are measurable, continuous almost everywhere with respect to the Lebesgue measure, and the diffusion coefficient may degenerate on some subsets of the domain.
Euler's Approximations of Weak Solutions of Reflecting SDEs with Discontinuous Coefficients
We study convergence in law for the Euler and Euler-Peano schemes for stochastic differential equations reflecting on the boundary of a general convex domain. We assume that the coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. The proofs are based on new estimates of Krylov's type for the approximations considered.
Évolution d'une file d'attente avec priorité
Evolution in random environment and structural instability.
Exact controllability for a nonlinear stochastic wave equation.
Exact simulation for solutions of one-dimensional Stochastic Differential Equations with discontinuous drift
In this note we propose an exact simulation algorithm for the solution of (1)d X t = d W t + b̅ ( X t ) d t, X 0 = x, where b̅is a smooth real function except at point 0 where b̅(0 + ) ≠ b̅(0 −) . The main idea is to sample an exact skeleton of Xusing an algorithm deduced from the convergence of the solutions of the skew perturbed equation (2)d X t β = d W t + b̅ ( X t β ) d t + β d L t 0 ( X β ) , X 0 = x towardsX solution of (1) as β ≠ 0 tends to 0. In this note, we show that this convergence...
Example of continuous second-order stochastic process with prescribed finite multiplicity
Excercises in stochastic analysis
Existence and asymptotic behaviour of some time-inhomogeneous diffusions
Let us consider a solution of a one-dimensional stochastic differential equation driven by a standard Brownian motion with time-inhomogeneous drift coefficient . This process can be viewed as a Brownian motion evolving in a potential, possibly singular, depending on time. We prove results on the existence and uniqueness of solution, study its asymptotic behaviour and made a precise description, in terms of parameters , and , of the recurrence, transience and convergence. More precisely, asymptotic...