Different from traditional multiple-input and multiple-output (MIMO) radar, the frequency diverse array MIMO (FDA-MIMO) radar generates beampattern that is dependent on both range and angle, making it applicable for joint range–angle estimation of targets. In this paper, we propose a novel time reversal based FDA-MIMO (TR-FDA-MIMO) approach for target detection. Based on the time reversal theory, the TR-FDA-MIMO signal model is established, the TR transmitting–receiving and signal processing procedure are analyzed, and the resulting range–angle spectra for targets imaging are acquired by utilizing the multiple signal classification algorithm. Numerical simulations are carried out for both single and multiple targets cases. The imaging resolution and robustness to the noise of the proposed approach are investigated and results are compared with conventional FDA-MIMO radar. It turned out that by cooperating with TR, the performance of FDA-MIMO radar for target range–angle estimation is effectively enhanced, consequently improving its applicability in practical target-detecting cases.

We construct a simple example, surely known to Harry Kesten, of an R-transient Markov chain on a countable state space S ∪ {δ}, where δ is absorbing. The transition matrix K on S is irreducible and strictly substochastic. We determine the Yaglom limit, that is, the limiting conditional behavior given nonabsorption. Each starting state x ∈ S results in a different Yaglom limit. Each Yaglom limit is an R-1-invariant quasi-stationary distribution, where R is the convergence parameter of K. Yaglom limits that depend on the starting state are related to a nontrivial R-1-Martin boundary.

It is shown that the celebrated result of Sparre Andersen for random walks and Lévy processes has intriguing consequences when the last time of the process in (-∞, 0], say σ, is added to the picture. In the case of no positive jumps this leads to six random times, all of which have the same distribution—the uniform distribution on [0, σ]. Surprisingly, this result does not appear in the literature, even though it is based on some classical observations concerning exchangeable increments.

This study explored the target sound source location at unknown situation and processed the received signal to determine the location of the target, including the reconstructed signal of source immediately. In this paper, it used triangulation sound sources localization and time reversal method (TRM) to reconstruct the source signals. The purpose is to use a sound source localization method with a simple device to quickly locate the position of the sound source. This method uses the microphone array to measure signal from the target sound source. Then, the sound source location is calculated and is indicated by Cartesian coordinates. The sound source location is then used to evaluate free field impulse response function which can replace the impulse response function used in time-reversal method. This process reduces the computation time greatly which makes possible for a real time source localization and source signal separation.

Consider a one-sided Markov additive process with an upper and a lower barrier, where each can be either reflecting or terminating. For both defective and nondefective processes, and all possible scenarios, we identify the corresponding potential measures, which help to generalize a number of results for one-sided Lévy processes. The resulting rather neat formulae have various applications in risk and queueing theories, and, in particular, they lead to quasistationary distributions of the corresponding processes.

We establish some interesting duality results for Markov-modulated fluid flow models. Though fluid flow models are continuous-state analogues of quasi-birth-and-death processes, some duality results do differ by the inclusion of a scaling factor.

We describe the processes obtained by time reversal of a class of stationary jump diffusion processes that model the dynamics of genetic variation in populations subject to repeated bottlenecks. Assuming that only one lineage survives each bottleneck, the forward process is a diffusion on [0,1] that jumps to the boundary before diffusing back into the interior. We show that the behavior of the time-reversed process depends on whether the boundaries are accessible to the diffusive motion of the forward process. If a boundary point is inaccessible to the forward diffusion then time reversal leads to a jump diffusion that jumps immediately into the interior whenever it arrives at that point. If, instead, a boundary point is accessible then the jumps off of that point are governed by a weighted local time of the time-reversed process.

By establishing general relationships between branching transformations (Harris-Sevastyanov, Lamperti-Ney, time reversals, and Asmussen-Sigman) and Markov chain transforms (Doob's h-transform, time reversal, and the cone dual), we discover a deeper connection between these transformations with harmonic functions and invariant measures for the process itself and its space-time process. We give a classification of the duals into Doob's h-transform, pathwise time reversal, and cone reversal. Explicit results are obtained for the linear fractional offspring distribution. Remarkably, for this case, all reversals turn out to be a Galton-Watson process with a dual reproduction law and eternal particle or some kind of immigration. In particular, we generalize a result of Klebaner and Sagitov (2002) in which only a geometric offspring distribution was considered. A new graphical representation in terms of an associated simple random walk on N2 allows for illuminating picture proofs of our main results concerning transformations of the linear fractional Galton-Watson process.

There are two types of Asian options in the financial markets which differ according to the role of the average price. We give a symmetry result between the floating- and fixed-strike Asian options. The proof involves a change of numéraire and time reversal of Brownian motion. Symmetries are very useful in option valuation, and in this case the result allows the use of more established fixed-strike pricing methods to price floating-strike Asian options.

In this paper we extend the class of zero-order threshold autoregressive models to a much richer class of mixture models. The new class has the important property of duality which, as we show, corresponds to time reversal. We are then able to obtain the time reversals of the zero-order threshold models and to characterise the time-reversible members of this subclass. These turn out to be quite trivial. The time-reversible models of the more general class do not suffer in this way. The complete stationary distributional structure is given, as are various moments, in particular the autocovariance function. This is shown to be of ARMA type. Finally we give two examples, the second of which extends from the finite to the countable mixture case. The general theory for this extension will be given elsewhere.

The mean busy period of a Markov-modulated queue or fluid model is computed by an extension of the time-reversal argument connecting the steady-state distribution and the maximum of a related Markov additive process.

We present conditions under which a point process of certain jump times of a Markov process is a Poisson process. The central idea is that if the Markov process is stationary and the compensator of the point process in reverse time has a constant intensity a, then the point process is Poisson with rate a. A known example is that the output flow from an M/M/1 queueing system is Poisson. We present similar Poisson characterizations of more general marked point process functionals of a Markov process. These results yield easy-to-use criteria for a collection of such processes to be multivariate Poisson, compound Poisson, or marked Poisson with a specified dependence or independence. We discuss several applications for queueing systems with batch arrivals and services and for networks of queues. We also indicate how our results extend to functionals of non-Markovian processes.

It is shown that, for one model of genetic evolution, the times at which mutations at nucleotide sites become fixed in a population tend to cluster together rather than behave as a Poisson process.

The connection between the age distribution of a discrete-time Markov chain and a certain time-reversed Markov chain is exhibited. A method for finding properties of age distributions follows simply from this approach. The results, which have application in several areas in applied probability, are illustrated by examples from population genetics.

The behaviour in equilibrium of networks of queues is studied. Equilibrium distributions are obtained and in certain cases it is shown that the state of an individual queue is independent of the state of the rest of the network. The processes considered in this paper are irreversible; however, the method used to establish equilibrium distributions is one which has previously only been used when dealing with reversible processes. Results are obtained for models of communication networks, machine interference and birth-illness-death processes.