Davis-type inequalities for a number of diffusion processes.
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.
Densité des diffusions en temps petit : développements asymptotiques (part I)
Dérivation par rapport au processus de Bessel
Differentiability of excessive functions of one-dimensional diffusions and the principle of smooth fit
The principle of smooth fit is probably the most used tool to find solutions to optimal stopping problems of one-dimensional diffusions. It is important, e.g., in financial mathematical applications to understand in which kind of models and problems smooth fit can fail. In this paper we connect-in case of one-dimensional diffusions-the validity of smooth fit and the differentiability of excessive functions. The basic tool to derive the results is the representation theory of excessive functions;...
Differential operators and spectral distributions of invariant ensembles from the classical orthogonal polynomials. The continuous case.
Diffusion approximation for first overflow time in system with finite capacity.
Diffusion approximations of the geometric Markov renewal processes and option price formulas.
Diffusion Limits Of Conditioned Critical Galton-Watson Processes.
Diffusion on the total space of a vector bundle.
Diffusion processes and second order elliptic operators with singular coefficients for lower order terms.
Diffusion with an reflecting and absorbing level set boundary - a simulation study
Diffusions à coefficients continus, d'après Stroock et Varadhan
Diffusions avec branchement et interaction
Diffusions hypercontractives
Diffusions in random environment and ballistic behavior
Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized burgers' equations
Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized Burgers' equations
We prove existence and uniqueness for two classes of martingale problems involving a nonlinear but bounded drift coefficient. In the first class, this coefficient depends on the time t, the position x and the marginal of the solution at time t. In the second, it depends on t, x and p(t,x), the density of the time marginal w.r.t. Lebesgue measure. As far as the dependence on t and x is concerned, no continuity assumption is made. The results, first proved for the identity diffusion matrix,...
Diffusions with measurement errors. I. Local asymptotic normality
We consider a diffusion process which is observed at times for , each observation being subject to a measurement error. All errors are independent and centered gaussian with known variance . There is an unknown parameter within the diffusion coefficient, to be estimated. In this first paper the case when is indeed a gaussian martingale is examined: we can prove that the LAN property holds under quite weak smoothness assumptions, with an explicit limiting Fisher information. What is perhaps...