A recurrence condition for some subordinated strongly local Dirichlet forms.
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 recursion formula for the moments of the gaussian orthogonal ensemble
We present an analogue of the Harer–Zagier recursion formula for the moments of the gaussian Orthogonal Ensemble in the form of a five term recurrence equation. The proof is based on simple gaussian integration by parts and differential equations on Laplace transforms. A similar recursion formula holds for the gaussian Symplectic Ensemble. As in the complex case, the result is interpreted as a recursion formula for the number of 1-vertex maps in locally orientable surfaces with a given number of...
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 normal approximation to Poisson binomial.
A refinement of the Helson-Szegö theorem and the determination of the extremal measures
A regeneration proof of the central limit theorem for uniformly ergodic Markov chains.
A relation between dimension of the harmonic measure, entropy and drift for a random walk on a hyperbolic space.
A relaxation theorem for partially observed stochastic control on Hilbert space
In this paper, we present a result on relaxability of partially observed control problems for infinite dimensional stochastic systems in a Hilbert space. This is motivated by the fact that measure valued controls, also known as relaxed controls, are difficult to construct practically and so one must inquire if it is possible to approximate the solutions corresponding to measure valued controls by those corresponding to ordinary controls. Our main result is the relaxation theorem which states that...
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 associative copulas
A method for producing associative copulas from a binary operation and a convex function on an interval is described.
A Remark on Buffon's Needle Problem.
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 metrics for finitely additive distribution functions.
A remark on Slutsky's theorem
A remark on stochastic integration
A remark on the class of martingales with bounded quadratic variation