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Let Y be a random variable whose moment-generating function exists in some neighborhood of the origin. While probabilistic Stirling numbers of the first and second kind have been introduced, early definitions often failed to satisfy…
Stochastic network calculus is the probabilistic version of the network calculus, which uses envelopes to perform probabilistic analysis of queueing networks. The accuracy of probabilistic end-to-end delay or backlog bounds computed using…
Opportunities for stochastic arbitrage in an options market arise when it is possible to construct a portfolio of options which provides a positive option premium and which, when combined with a direct investment in the underlying asset,…
A logarithmic type Harnack inequality is established for the semigroup of solutions to a stochastic differential equation in Hilbert spaces with non-additive noise. As applications, the strong Feller property as well as the entropy-cost…
This work is about a new class of martingales: the vertical martingales. We construct the vertical martingale for smooth submersions and we develop a stochastic calculus for one. Furthermore, we gives a stochastic characterization for…
This paper provides a characterization of all possible dependency structures between two stochastically ordered random variables. The answer is given in terms of copulas that are compatible with the stochastic order and the marginal…
We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…
We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…
This paper does not suppose a priori that the evolution of the price of a financial asset is a semimartingale. Since possible strategies of investors are self-financing, previous prices are forced to be finite quadratic variation processes.…
A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…
Determining functionals are tools to describe the finite dimensional long-term dynamics of infinite dimensional dynamical systems. There also exist several applications to infinite dimensional {\em random} dynamical systems. In these…
Some classes of increment martingales, and the corresponding localized classes, are studied. An increment martingale is indexed by the real line and its increment processes are martingales. We focus primarily on the behavior as time goes to…
The Feynman integral is given a stochastic interpretation in the framework of Nelson's stochastic mechanics employing a time-symmetric variant of Nelson's kinematics recently developed by the author.
This paper is devoted to the construction of exponential integrators of first and second order for the time discretization of constrained parabolic systems. For this extend, we combine well-known exponential integrators for unconstrained…
We present a way of introducing joint distibution function and its marginal distribution functions for non-compatible observables. Each such marginal distribution function has the property of commutativity. Models based on this approach can…
We develop a martingale approach for studying continuous-time stochastic differential games of control and stopping, in a non-Markovian framework and with the control affecting only the drift term of the state-process. Under appropriate…
The paper examines the construction and analysis of a new class of mixed exponential statistical structures that combine the properties of stochastic models and linear positive operators. The relevance of the topic is driven by the growing…
A new tool for modeling electrochemical kinetics is presented. An extension of the Stochastic Simulation Algorithm framework to electrochemical systems is proposed. The physical justifications and constraints for the derivation of a…
In this paper, we introduce a new two-parameter lifetime distribution, called the exponential-generalized truncated logarithmic (EGTL) distribution, by compounding the exponential and generalized truncated logarithmic distributions. Our…
Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…