An application of the voter model–super-brownian motion invariance principle
An application of two-parameter martingales in harmonic analysis
Some duality results and some inequalities are proved for two-parameter Vilenkin martingales, for Fourier backwards martingales and for Vilenkin and Fourier coefficients.
An approach to the stochastic calculus in the non-Gaussian case.
An Approach to Wealth Modelling
2000 Mathematics Subject Classification: 60G48, 60G20, 60G15, 60G17. JEL Classification: G10The change in the wealth of a market agent (an investor, a company, a bank etc.) in an economy is a popular topic in finance. In this paper, we propose a general stochastic model describing the wealth process and give some of its properties and special cases. A result regarding the probability of default within the framework of the model is also offered.
An Arzela-Ascoli type theorem for random functions.
An asymptotic bound for the tail of the distribution of the maximum of a gaussian process
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 asymptotic test for quantitative gene detection
An Edgeworth expansion for a sum of m-dependent random variables.
An elementary proof of the Dalang-Morton-Willinger theorem
L. C. G. Rogers has given an elementary proof of the fundamental theorem of asset pricing in the case of finite discrete time, due originally to Dalang, Morton and Willinger. The purpose of this paper is to give an even simpler proof of this important theorem without using the existence of regular conditional distribution, in contrast to Rogers' proof.
An elementary property of conditional mathematical expectation. Application to the linear regularity of stochastic processes
An essay on the general theory of stochastic processes.
An example of a weak Bernoulli process which is not finitary
An Example of Quantum Exponential Process.
An explicit representation of the extended Skorokhod map with two time-dependent boundaries.
An exponential martingale equation.
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 a Meyer's theorem
An extension of an inequality due to Stein and Lepingle
Hardy spaces consisting of adapted function sequences and generated by the q-variation and by the conditional q-variation are considered. Their dual spaces are characterized and an inequality due to Stein and Lepingle is extended.