2 Review of probability. 5 2.1 Properties of expectation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Convergence of random variables. . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Convergence in probability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.4 Norms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Informati...

In this paper, we study Dirichlet operators on certain smooth Banach spaces. We establish the well-known Kato's inequality in our general infinite dimensional setting. By applying this,we show the essential self-adjointness of Dirichlet operators with non-constant diffusion part on certain smooth Banach spaces. We also provide an approximation criterion for essential self-adjointness of Dirichl...

A difference approximation that is second-order accurate in the time step h is derived for the general Ito stochastic differential equation. The difference equation has the form of a second-order random walk in which the random terms are non-linear combinations of Gaussian random variables. For a wide class of problems, the transition pdf is joint-normal to second order in h; the technique then...

The Metropolis–Hastings algorithm was applied to a standard Virtual Population Analysis using a simulated data set containing catch data from 10 age groups over a 10-year period. Posterior distributions of fishing mortalities and population sizes are studied under different prior assumptions. The results demonstrate the usefulness of obtaining distributions of plausible parameter values instead...

We tightly analyze the sample complexity of CCA, provide a learning algorithm that achieves optimal statistical performance in time linear in the required number of samples (up to log factors), as well as a streaming algorithm with similar guarantees.

We investigate some graph properties which may simplify the computation of the steady-state distribution of Markov chain. We consider the directed graph associated to a Markov chain derived from Stochastic Automata Network and we give an algorithm to solve the Kolmogorov equations for the steady-state distribution. Then, we present an extension of this algorithm which allows the parametric anal...

The world we live in has never been very predictable, and randomness has always been part of our lives. There is ample evidence that our ancestors did enjoy playing games of chance, and the early development of probability theory had to do with these games. The study of probability has always been motivated by potential applications. Besides gambling, the stimulus has come from life insurance, ...

In this article, we study the discounted penalty at ruin in a perturbed compound Poisson model with two-sided jumps. We show that it satisfies a renewal equation under suitable conditions and consider an application of this renewal equation to study some perpetual American options. In particular, our renewal equation gives a generalization of the renewal equation in Gerber and Landry [2] where ...