Degenerate stochastic differential equations arising from catalytic branching networks.
Degenerate stochastic differential equations for catalytic branching networks
Uniqueness of the martingale problem corresponding to a degenerate SDE which models catalytic branching networks is proven. This work is an extension of the paper by Dawson and Perkins [Illinois J. Math.50 (2006) 323–383] to arbitrary catalytic branching networks. As part of the proof estimates on the corresponding semigroup are found in terms of weighted Hölder norms for arbitrary networks, which are proven to be equivalent to the semigroup norm for this generalized setting.
Delay equations driven by rough paths.
Densité des diffusions en temps petit : développements asymptotiques (part I)
Dérivation stochastique de diffusions réfléchies
Deterministic characterization of viability for stochastic differential equation driven by fractional brownian motion
In this paper, using direct and inverse images for fractional stochastic tangent sets, we establish the deterministic necessary and sufficient conditions which control that the solution of a given stochastic differential equation driven by the fractional Brownian motion evolves in some particular sets K. As a consequence, a comparison theorem is obtained.
Développement asymptotique de la densité d'une diffusion dégénérée.
Differential equations driven by gaussian signals
We consider multi-dimensional gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of Lévy area(s). gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful – yet conceptually simple – framework in which to analyze differential equations driven by gaussian signals in the rough paths sense.
Differential equations driven by rough signals.
This paper aims to provide a systematic approach to the treatment of differential equations of the typedyt = Σi fi(yt) dxti where the driving signal xt is a rough path. Such equations are very common and occur particularly frequently in probability where the driving signal might be a vector valued Brownian motion, semi-martingale or similar process.However, our approach is deterministic, is totally independent of probability and permits much rougher paths than the Brownian paths usually discussed....
Differentiation of measures.
Diffusion de sphères dures dans la droite réelle : comportement macroscopique et équilibre local
Diffusion with an reflecting and absorbing level set boundary - a simulation study
Discrete approximations of generalized RBSDE with random terminal time
The convergence of discrete approximations of generalized reflected backward stochastic differential equations with random terminal time in a general convex domain is studied. Applications to investigation obstacle elliptic problem with Neumann boundary condition for partial differential equations are given.
Discrete Approximations of Strong Solutions of Reflecting SDEs with Discontinuous Coefficients
We study convergence for the Euler scheme for stochastic differential equations reflecting on the boundary of a general convex domain D ⊆ ℝd. We assume that the equation has the pathwise uniqueness property and its coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. In the case D=[0,∞) new sufficient conditions ensuring pathwise uniqueness for equations with possibly discontinuous coefficients are given.
Discrétisation d'une équation différentielle stochastique et calcul approché d'espérances de fonctionnelles de la solution
Discretizing a backward stochastic differential equation.
Distributions of functionals of diffusions with jumps.
Distribution-Valued Processes Arising from Independent Brownian Motions.
Donsker-type theorem for BSDEs.
Double-barriers-reflected BSDEs with jumps and viscosity solutions of parabolic integrodifferential PDEs.