State space calculations for discrete probability densities

Modelling non-negative discrete valued for time series analysis was introduced by previous researchers, that is Integer-Valued Autoregressive (INAR) model. The model involves both the parameter index and state space are discrete. Various phenomena within the scope of discrete cases are not only affected by previous discrete observations, but also affected by the discrete observations at surrounding locations in previous time. As a result, this model involves two parameter indices namely time and space, and also state space which are discrete. In continuous cases, a model has been introduced to overcome this problem, namely Generalized Space Time Autoregressive (GSTAR) model (discrete parameter index and continuous state space). Using this model to solve the discrete case produces a continuous forecast value, so it needs a discretization process. In the time series model for discrete cases, thinning operators have been introduced as a substitute for discretization in a continuous time series. The thinning operator paradigm in the discrete time series will be developed in the space-time model proposed in this paper. This paper will also introduce a new model, namely a space-time model for cases related to discrete cases. This means that the index of time and location parameters, as well as the state space used is a discrete state space. The properties that apply to the model are adopted from the INAR model and the GSTAR model for continuous cases. The main focus of this paper is the development of thinning operators from time series to space-time models. This paper also provides a modeling procedure using the GSTAR model for discrete cases. The result of this paper is the formation of a GSTAR model with a discrete state space.

Subspace algorithms are used for the identification of linear, time invariant, finite dimensional, discrete time state space systems. In the identification the order of the estimated system has to be specified. This paper provides a criterion for choosing the order. The asymptotic properties of the examined procedure are derived under appropriate assumptions on the data generating process. It is shown, that the criterion leads to asymptotically consistent estimates of the order only in a generic case. In a simulation study the effects of some user choices on the performance of the order estimates is demonstrated.

A Local Volatility Model to Price and Calibrate Year-on-Year and Zero-Coupon Inflation Options

In the literature concerning Dirichlet forms and its applications, closability plays a crucial role. In fact, closedness is one of the defining properties of a Dirichlet form. According to this, a number of closability criterions are known in particular cases. An important question is under which conditions closability is kept after changing the reference measure. M. Fukushima, K. Sato, and S. Taniguchi [5] treated this problem for a regular Dirichlet form (E (E )) which is defined on a locally compact separable metric state space. Under technical conditions on some core C ⊆ (E ), they presented a complete solution if the Dirichlet form is either irreducible or transient. An earlier paper dealing with this subject is M. Rockner and N. Wielens [13]. Related results on Lusinean separable metric spaces were published in I. Shigekawa and S. Taniguchi [16]. The aim of this paper is to give general analytical conditions in order to keep closability when turning to a new reference measure. One particular purpose is to present an extension of an assertions in [5] (namely, Corollary 4.2) within a purely measure theoretic framework, i.e., the state space ( B) is just a measurable space. In particular, the set C is defined exclusively in terms of the initial form (E (E )) on 2( μ). The main results are Theorems 2.3, 2.4, and 2.5. We proceed to give some basic definitions.

When an autonomous robot is to learn its behavior, whether an appropriate state space is available or not is a critical issue for the flexibility and efficiency of the learning process. What is problematic is that it is usually very difficult to prepare such an ideal state space manually beforehand. We propose a new state space method. With this, behavior-based robots can autonomously rebuild their state spaces after they accumulate behavior experience using initial state spaces. This reconstruction approach is more advantageous than the conventional state space construction methods or incremental state partitioning methods in that it achieves both the efficiency in the learning process and the optimality of the resultant behavior performance.

Newton’s law of cooling requires a reference temperature (Tref) to define the heat-transfer coefficient (h). For external flows with multiple temperatures in the freestream, obtaining Tref is a challenge. One widely used method, referred to as the adiabatic-wall (AW) method, obtains Tref by requiring the surface of the solid exposed to convective heat transfer to be adiabatic. Another widely used method, referred to as the linear-extrapolation (LE) method, obtains Tref by measuring/computing the heat flux (qs′′) on the solid surface at two different surface temperatures (Ts) and then linearly extrapolating to qs′′=0. A third recently developed method, referred to as the state-space (SS) method, obtains Tref by probing the temperature space between the highest and lowest in the flow to account for the effects of Ts or qs′′ on Tref. This study examines the foundation and accuracy of these methods via a test problem involving film cooling of a flat plate where qs′′ switches signs on the plate’s surface. Results obtained show that only the SS method could guarantee a unique and physically meaningful Tref where Ts=Tref on a nonadiabatic surface qs′′=0. The AW and LE methods both assume Tref to be independent of Ts, which the SS method shows to be incorrect. Though this study also showed the adiabatic-wall temperature, TAW, to be a good approximation of Tref (<10% relative error), huge errors can occur in h about the solid surface where |Ts−TAW| is near zero because where Ts=TAW, qs′′≠0.

Quantifying ecological thresholds from response surfaces

Intelligent fault detection of reciprocating compressor using a novel discrete state space

A State Space Boundary Element Method with Analytical Formulas for Nearly Singular Integrals

Deep reinforcement learning based planning method in state space for lunar rovers

In this paper, we show how to approximate Heath–Jarrow–Morton dynamics for the forward prices in commodity markets with arbitrage-free models which have a finite-dimensional state space. Moreover, we recover a closed-form representation of the forward price dynamics in the approximation models and derive the rate of convergence to the true dynamics uniformly over an interval of time to maturity under certain additional smoothness conditions. In the Markovian case, we can strengthen the convergence to be uniform over time as well. Our results are based on the construction of a convenient Riesz basis on the state space of the term structure dynamics.

This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A, M, phi), where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively, and phi generalizes the concept of the z-transform to bijective linear mappings from a vector space of, e.g., signal samples, into the module M. A signal model provides the structure for a particular linear signal processing application, such as infinite and finite discrete time, or infinite or finite discrete space, or the various forms of multidimensional linear signal processing. As soon as a signal model is chosen, basic ingredients follow, including the associated notions of filtering, spectrum, and Fourier transform. The shift operator is a key concept in the algebraic theory: it is the generator of the algebra of filters A. Once the shift is chosen, a well-defined methodology leads to the associated signal model. Different shifts correspond to infinite and finite time models with associated infinite and finite z-transforms, and to infinite and finite space models with associated infinite and finite C-transforms (that we introduce). In particular, we show that the 16 discrete cosine and sine transforms are Fourier transforms for the finite space models. Other definitions of the shift naturally lead to new signal models and to new transforms as associated Fourier transforms in one and higher dimensions, separable and non-separable. We explain in algebraic terms shift-invariance (the algebra of filters A is commutative), the role of boundary conditions and signal extensions, the connections between linear transforms and linear finite Gauss-Markov fields, and several other concepts and connections.

We consider the task of filtering a dynamic parameter evolving as a diffusion process, given data collected at discrete times from a likelihood which is conjugate to the reversible law of the diffusion, when a generic dual process on a discrete state space is available. Recently, it was shown that duality with respect to a death-like process implies that the filtering distributions are finite mixtures, making exact filtering and smoothing feasible through recursive algorithms with polynomial complexity in the number of observations. Here we provide general results for the case where the dual is a regular jump continuous-time Markov chain on a discrete state space, which typically leads to filtering distribution given by countable mixtures indexed by the dual process state space. We investigate the performance of several approximation strategies on two hidden Markov models driven by Cox–Ingersoll–Ross and Wright–Fisher diffusions, which admit duals of birth-and-death type, and compare them with the available exact strategies based on death-type duals and with bootstrap particle filtering on the diffusion state space as a general benchmark.

Acceleration of cellular automata algorithms using genetic algorithms

The state space model provides an unifying framework for analyzing time series. For the classical Box–Jenkins analysis, state space methods are useful when estimating the autoregressive and moving average coefficients by exact maximum likelihood and when missing values are present. In the case of unobserved components time series models with interpretable components such as trend, seasonal, cycle and irregular, state space methods provide the tools for estimation, signal extraction and diagnostic checking. Indeed, all linear time series models can be cast into state space including dynamic regression models and cubic spline smoothing models.