A random walk on the rook placements on a Ferrers board.
A rate-optimal trigonometric series expansion of the fractional Brownian motion.
A recurrence theorem for square-integrable martingales
Let be a zero-mean martingale with canonical filtration and stochastically -bounded increments which means that a.s. for all n ≥ 1, t > 0 and some square-integrable distribution H on [0,∞). Let . It is the main result of this paper that each such martingale is a.s. convergent on V < ∞ and recurrent on V = ∞, i.e. for some c > 0. This generalizes a recent result by Durrett, Kesten and Lawler [4] who consider the case of only finitely many square-integrable increment distributions....
A recursive robust Bayesian estimation in partially observed financial market
I propose a nonlinear Bayesian methodology to estimate the latent states which are partially observed in financial market. The distinguishable character of my methodology is that the recursive Bayesian estimation can be represented by some deterministic partial differential equation (PDE) (or evolution equation in the general case) parameterized by the underlying observation path. Unlike the traditional stochastic filtering equation, this dynamical representation is continuously dependent on the...
A refinement of the Helson-Szegö theorem and the determination of the extremal measures
A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space.
A remark concerning random walks with random potentials
We consider random walks where each path is equipped with a random weight which is stationary and independent in space and time. We show that under some assumptions the arising probability distributions are in a sense uniformly absolutely continuous with respect to the usual probability distribution for symmetric random walks.
A remark concerning uniqueness of the Wold decomposition of finite-dimensional stationary processes.
The uniqueness of the Wold decomposition of a finite-dimensional stationary process without assumption of full rank stationary process and the Lebesgue decomposition of its spectral measure is easily obtained.
A remark on a problem of Girsanov
A remark on disjointness results for stable processes
A remark on F. B. Knight's paper : “A post-predictive view of gaussian processes”
A remark on the class of martingales with bounded quadratic variation
A remark on the equivalence of Gaussian processes.
A remark on the norm of a random walk on surface groups
We show that the norm of the random walk operator on the Cayley graph of the surface group in the standard presentation is bounded by 1/√g where g is the genus of the surface.
A remark on the paper “Une martingale d'opérateurs bornés, non représentable en intégrale stochastique”, by J.L. Journé and P.A. Meyer
A remark on the r-th mean differentiability.
A Remark on the Strong Law of Large Numbers.
A remark on the weighted averages for superadditive processes.
A remark on Tsirelson's stochastic differential equation
A remarkable -finite measure unifying supremum penalisations for a stable Lévy process
The -finite measure which unifies supremum penalisations for a stable Lévy process is introduced. Silverstein’s coinvariant and coharmonic functions for Lévy processes and Chaumont’s -transform processes with respect to these functions are utilized for the construction of .