A characterization of Gaussian processes that are Markovian
A Class of Contractions in Hilbert Space and Applications
We characterize the bounded linear operators T in Hilbert space which satisfy T = βI + (1-β)S where β ∈ (0,1) and S is a contraction. The characterizations include a quadratic form inequality, and a domination condition of the discrete semigroup by the continuous semigroup . Moreover, we give a stronger quadratic form inequality which ensures that . The results apply to large classes of Markov operators on countable spaces or on locally compact groups.
A connection between Gaussian processes and Markov processes.
A conservative evolution of the Brownian excursion.
A constructive sharp approach to functional quantization of stochastic processes.
A different construction of gaussian fields from Markov chains : Dirichlet covariances
A Gaussian correlation inequality and its applications to small ball probabilities.
A generalized mean-reverting equation and applications
Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with Hölder continuous paths on [0,T] (T> 0). Taking that equation in rough paths sense only gives local existence of the solution because the non-explosion condition is not satisfied in general. Under natural assumptions, by using specific methods, we show the global existence and uniqueness of the solution, its integrability, the continuity and differentiability of the...
A growth estimate for continuous random fields
We prove a polynomial growth estimate for random fields satisfying the Kolmogorov continuity test. As an application we are able to estimate the growth of the solution to the Cauchy problem for a stochastic diffusion equation.
A limit theorem for joint distribution of order-statistics from stationary Gaussian sequences
A limit theorem for maxima of nonstationary Gaussian sequences
A Markov property for two parameter Gaussian processes.
This paper deals with the relationship between two-dimensional parameter Gaussian random fields verifying a particular Markov property and the solutions of stochastic differential equations. In the non Gaussian case some diffusion conditions are introduced, obtaining a backward equation for the evolution of transition probability functions.
A new intrinsic construction of the gaussian measure in ; with application
A note on ergodic transformations of self-similar Volterra Gaussian processes.
A Note on Functions Which Separate Gaussian Measures.
A note on Gauss measures which agree on small balls
A post-predictive view of gaussian processes
A probabilistic approach to the asymptotics of the length of the longest alternating subsequence.
A rate-optimal trigonometric series expansion of the fractional Brownian motion.
A remark on F. B. Knight's paper : “A post-predictive view of gaussian processes”