An application of the voter model–super-brownian motion invariance principle
An approximation scheme for the optimal control of diffusion processes
An asymptotic expansion for the discrete harmonic potential.
An asymptotic expansion for the distribution of the supremum of a random walk
Let be a random walk drifting to -∞. We obtain an asymptotic expansion for the distribution of the supremum of which takes into account the influence of the roots of the equation being the underlying distribution. An estimate, of considerable generality, is given for the remainder term by means of submultiplicative weight functions. A similar problem for the stationary distribution of an oscillating random walk is also considered. The proofs rely on two general theorems for Laplace transforms....
An elementary proof of Hawkes's conjecture on Galton-Watson trees.
An equation involving local time
An ergodic theorem for a class of spin systems
An expectation maximization algorithm to model failure times by continuous-time Markov chains.
An explicit representation of the extended Skorokhod map with two time-dependent boundaries.
An extended generator and Schrödinger equations.
An extension of a boundedness result for singular integral operators
We study some operators originating from classical Littlewood-Paley theory. We consider their modification with respect to our discontinuous setup, where the underlying process is the product of a one-dimensional Brownian motion and a d-dimensional symmetric stable process. Two operators in focus are the G* and area functionals. Using the results obtained in our previous paper, we show that these operators are bounded on . Moreover, we generalize a classical multiplier theorem by weakening its...
An extension of Krein's inverse spectral theorem to strings with nonreflecting left boundaries
An extension of Motoo's theorem
An extension of the Yamada-Watanabe condition for pathwise uniqueness to stochastic differential equations with jumps.
An extreme-value analysis of the LIL for Brownian motion.
An integral representation of randomized probabilities and its applications
An integral test for the transience of a brownian path with limited local time
We study a one-dimensional brownian motion conditioned on a self-repelling behaviour. Given a nondecreasing positive function f(t), t≥0, consider the measures μt obtained by conditioning a brownian path so that Ls≤f(s), for all s≤t, where Ls is the local time spent at the origin by time s. It is shown that the measures μt are tight, and that any weak limit of μt as t→∞ is transient provided that t−3/2f(t) is integrable. We conjecture that this condition is sharp and present a number of open problems....
An interacting particles process for Burgers equation on the circle.
An invariance principle for Markov processes and brownian particles with singular interaction
An invariance principle for the law of the iterated logarithm for some Markov chains
Strassen's invariance principle for additive functionals of Markov chains with spectral gap in the Wasserstein metric is proved.