This is a study of the existence of bifurcation branches for the problem of finding even, periodic solutions in fourth-order, reversible Hamiltonian systems such that the Hamiltonian evaluates to zero along each solution on the branch. The class considered here is a generalization of both the Swift–Hohenberg and extended Fisher–Kolmogorov equations that have been studied in several recent paper...

We consider two player electromagnetic evasion-pursuit games where each player must incorporate significant uncertainty into their design strategies to disguise their intension and confuse their opponent. In this paper, the evader is allowed to make dynamic changes to his strategies in response to the dynamic input with uncertainty from the interrogator. The problem is formulated in two differe...

The existence of a moment function satisfying a drift function condition is well-known to guarantee non-explosiveness of the associated minimal Markov process (cf.[1, 6]), under standard technical conditions. Surprisingly, the reverse is true as well for a countable space Markov process. We prove this result by showing that recurrence of an associated jump process, that we call the α-jump proce...

In this paper we study stochastic models for the transport of particles in a uidized bed reactor, and compute the associated residence time distribution (RTD). Our main model is basically a diiusion process in 0; A] with reeecting/absorbing boundary conditions, modiied by allowing jumps to the origin as a result of transport of particles in the wake of rising uidization bubbles. We study discre...

This paper deals with the general optimal control problem for fully coupled forward-backward stochastic differential equations with random jumps FBSDEJs . The control domain is not assumed to be convex, and the control variable appears in both diffusion and jump coefficients of the forward equation. Necessary conditions of Pontraygin’s type for the optimal controls are derived by means of spike...

Space-time variational formulations and adaptive Wiener–Hermite polynomial chaos Galerkin discretizations of Kolmogorov equations in infinite dimensions, such as Fokker–Planck andOrnstein–Uhlenbeck equations for functions defined on an infinite-dimensional separable Hilbert space H , are developed. The wellposedness of these equations in the Hilbert space L2(H, μ) of functions on the infinite-d...

In [5] the authors obtained Mean-Field backward stochastic differential equations (BSDE) associated with a Mean-field stochastic differential equation (SDE) in a natural way as limit of some highly dimensional system of forward and backward SDEs, corresponding to a large number of “particles” (or “agents”). The objective of the present paper is to deepen the investigation of such Mean-Field BSD...

We study in this paper a TCP-like linear-increase multiplicative-decrease flow control mechanism. We consider congestion signals that arrive in batches according to a Poisson process. We focus on the case when the transmission rate cannot exceed a certain maximum value. We write the Kolmogorov equations and we use Laplace Transforms to calculate the distribution of the transmission rate in the ...

This work presents probabilistic methods for testability analysis at RTL and their use to evaluate the sensitivity of a digital circuit to Single Event Upsets (SEUs). A new probabilistic testability metric is proposed, in order to evaluate if the possible changes caused by SEUs are ignored or propagated by the dynamic behavior of the circuit. The new metric, event detectability, is defined base...

Motivated by earlier work on the use of fully-coupled Forward-Backward Stochastic Differential Equations (henceforth FBSDEs) in the analysis of mathematical models for the CO2 emissions markets, the present study is concerned with the analysis of these equations when the generator of the forward equation has a conservative degenerate structure and the terminal condition of the backward equation...