Financial Technology (FinTech) is considered a taxonomy that describes a wide range of ICT (information and communications technology) associated with financial transactions and related operations. Improvement of service quality is the main issue addressed in this taxonomy, and there are a large number of emerging technologies including blockchain-based cryptocurrencies and smart contracts. Due to its innovative nature in accounting, blockchain can also be used in lots of other FinTech contexts where token models play an important role for financial engineering. This paper revisits some of the key concepts accumulated behind this trend, and shows a generalized understanding of the technology using an adapted stochastic process. With a focus on financial instruments using blockchain, research directions toward stable applications are identified with the help of a newly proposed stabilizer: interpretation function of token valuation. The idea of adapted stochastic process is essential for the stabilizer, too.

Randomly distributed wireless sensors used to monitor and detect a moving object were investigated, and performance measures such as the expected time/space detection ratio were theoretically analyzed. In particular, the insensitivities (robustness) of the performance measures to the conditions of the distributed wireless sensors and the target object were analyzed. Robust explicit equations for these performance measures were derived, and these equations can be used to calculate them without knowing the sensing area shape or the target object trajectory. These equations were applied to the following two applications. (1) They were used to estimate the impact of active/sleeping state schedule algorithms of sensors on the expected ratio of the time that the sensors detect the target object during its movement. The results were used to identify the active state schedule that increases the expected time ratio. (2) They were also applied to a sensor density design method that uses a test object. This method can be used to ensure that the expected time ratio that at least one sensor can detect the target satisfies the target value without knowing the sensing area size or the movement of the target object.

In this letter, we define the generalized doubly stochastic processing via Jacket matrices of order-2n and 2n with the integer, n≥2. Different from the Hadamard factorization scheme, we propose a more general case to obtain a set of doubly stochastic matrices according to decomposition of the fundaments of Jacket matrices. From order-2n and order-2n Jacket matrices, we always have the orthostochastoc case, which is the same as that of the Hadamard matrices, if the eigenvalue λ1 = 1, the other ones are zeros. In the case of doubly stochastic, the eigenvalues should lead to nonnegative elements in the probability matrix. The results can be applied to stochastic signal processing, pattern analysis and orthogonal designs.

Since their inception almost fifty years ago, hidden Markov models (HMMs) have have become the predominant methodology for automatic speech recognition (ASR) systems--today, most state-of-the-art speech systems are HMM-based. There have been a number of ways to explain HMMs and to list their capabilities, each of these ways having both advantages and disadvantages. In an effort to better understand what HMMs can do, this tutorial article analyzes HMMs by exploring a definition of HMMs in terms of random variables and conditional independence assumptions. We prefer this definition as it allows us to reason more throughly about the capabilities of HMMs. In particular, it is possible to deduce that there are, in theory at least, no limitations to the class of probability distributions representable by HMMs. This paper concludes that, in search of a model to supersede the HMM (say for ASR), rather than trying to correct for HMM limitations in the general case, new models should be found based on their potential for better parsimony, computational requirements, and noise insensitivity.

We propose a stochastic model for signals generated through the electron multiplying effect of detectors in charged particle beam equipments. This model is based on a stochastic variable characterized by a log-normal type distribution. The model is simple and can be used to represent a wide dynamic range of signals from pulse-like signals when the primary beam current is small to continuous signals when the primary beam current is large. For the model base reference a normalization of actual signal detectors is presented. This base reference yields the unique stochastic parameter used in our model. The proposed model better approximates the actual signals in the power spectrum distribution as compared to the filtered Poisson method presented elsewhere.

This paper investigates the stochastic property of the packet destinations and proposes an address generation algorithm which is applicable for describing various Internet access patterns. We assume that a stochastic process of Internet access satisfies the stationary condition and derive the fundamental structure of the address generation algorithm. Pseudo IP-address sequence generated from our algorithm gives dependable cache performance and reproduces the results obtained from trace-driven simulation. The proposed algorithm is applicable not only to the destination IP address but also to the destination URLs of packets, and is useful for simulation studies of Internet performance, Web caching, DNS, and so on.

We propose a new sampling method for 2D and 3D implicit surfaces. The method is based on a stochastic process defined by the Langevin equation with a Gaussian random-force term. Our Langevin equation describes a stochastic-dynamical particle, which develops in time confined around the sampled implicit surface with small width. Its numerically generated solutions can be easily moved onto the surface strictly with very few iteration of the Newton correction. The method is robust in a sense that an arbitrary number of sample points can be obtained starting from one simple initial condition. It is because (1) the time development of the stochastic-dynamical particle does not terminate even when it reaches the sampled implicit surface, and (2) there is non-zero transition probability from one disconnected component to another. The method works very well for implicit surfaces which are complicated topologically, mathematically, and/or in shape. It also has some advantageous features in rendering 3D implicit surfaces. Many examples of applying our sampling method to real 2D and 3D implicit surfaces are presented.

A review of research, covering about 50 years, about random phenomena in nonlinear dynamical systems and the problems of modeling such phenomena using real (as contrasted to abstract, axiomatic) mathematics. Private views of the author concerning personalities and events.

This work presents a further development of the approach to modelling thermal (i.e. carrier-velocity-fluctuation) noise in semiconductor devices proposed in papers by the present authors. The basic idea of the approach is to apply classical theory of Ito's stochastic differential equations (SDEs) and stochastic diffusion processes to describe noise in devices and circuits. This innovative combination enables to form consistent mathematical basis of the noise research and involve a great variety of results and methods of the well-known mathematical theory in device/circuit design. The above combination also makes our approach completely different, on the one hand, from standard engineering formulae which are not associated with any consistent mathematical modelling and, on the other hand, from the treatments in theoretical physics which are not aimed at device/circuit models and design. (Both these directions are discussed in more detail in Sect. 1). The present work considers the bipolar transistor compact model derived in Ref. [2] according to theory of Ito's SDEs and stochastic diffusion processes (including celebrated Kolmogorov's equations). It is shown that the compact model is transformed into the Ito SDE system. An iterative method to determine noisy currents as entries of the stationary stochastic process corresponding to the above Ito system is proposed.

This work deals with thermal-noise modeling for silicon vertical bipolar junction transistors (BJTs) and relevant integrated circuits (ICs) operating at low currents. The two-junction BJT compact model is consistently derived from the thermal-noise generalization of the Shockley semiconductor equations developed in work which treats thermal noise as the noise associated with carrier velocity fluctuations. This model describes BJT with the Itô non-linear stochastic-differential-equation (SDE) system and is suitable for large-signal large-fluctuation analysis. It is shown that thermal noise in silicon p-n-junction diode contributes to "microplasma" noise. The above model opens way for a consistent-modeling-based design/optimization of bipolar device noise performance with the help of theory of Itô's SDEs.

A stochastic system represented by an input-output model can be described by mainly two different types of state space representation. Corresponding to state space representations innovation models are examined. The relationship between both representations is made clear systematically. An easy transformation between them is presented. Zeros of innovation models are the same as those of an ARMA model which is stochastically equivalent to innovation models, and related to stable eigenvalues of generalized eigenvalue problem of matrix Riccati equation.

This paper proposes a second order auto-regressive equation with discrete-valued random coefficients. The auto-regressive equation transforms an independent stochastic sequence into a binary sequence, which is a special case of a stationary Markov chain. The power spectrum, correlation function and the transition probability are explicitly obtained in terms of the random coefficients. Some computer results are illustrated in figures.

Video service is slated to be a major application of emerging high-speed communications networks of the future. In particular, full-motion video is designed to take advantage of the high bandwidths that will become affordably available with the advent of B-ISDN. A salient feature of compressed video sources is that they give rise to autocorrelated traffic streams, which are difficult to model with traditional modeling techniques. In this paper, we describe a new methodology, called TES (Transform-Expand-Sample) , for modeling general autocorrelated time series, and we apply it to traffic modeling of compressed video. The main characteristic of this methodology is that it can model an arbitrary marginal distribution and approximate the autocorrelation structure of an empirical sample such as traffic measurements. Furthermore, the empirical marginal (histogram) and leading autocorrelations are captured simultaneously. Practical TES modeling is computationally intensive and is effectively carried out with software support. A computerized modeling environment, called TEStool, is briefly reviewed. TEStool supports a heuristic search approach for fitting a TES model to empirical time series. Finally, we exemplify our approach by two examples of TES video source models, constructed from empirical codec bitrate measurements: one at the frame level and the other at the group-of-block level. The examples demonstrate the efficacy of the TES modeling methodology and the TEStool modeling environment.