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 example of the decomposability semigroup
An existence result for a linear abstract stochastic equation in Hilbert spaces
An existence theorem for a stochastic partial differential equation arising from filtering theory
An expectation maximization algorithm to model failure times by continuous-time Markov chains.
An explicit formula about the convex hull of random points.
An explicit representation of the extended Skorokhod map with two time-dependent boundaries.
An exponential inequality for negatively associated random variables.
An exponential martingale equation.
An extended generator and Schrödinger equations.
An extended problem to Bertrand's paradox
Bertrand's paradox is a longstanding problem within the classical interpretation of probability theory. The solutions 1/2, 1/3, and 1/4 were proposed using three different approaches to model the problem. In this article, an extended problem, of which Bertrand's paradox is a special case, is proposed and solved. For the special case, it is shown that the corresponding solution is 1/3. Moreover, the reasons of inconsistency are discussed and a proper modeling approach is determined by careful examination...
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 a result of Csiszár.
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.
An extension of Billingsley’s uniform boundedness theorem to higher-dimensional -processes
An extension of Chebyshev's inequality
An extension of Krein's inverse spectral theorem to strings with nonreflecting left boundaries