scholarly journals FROM BOUNDARY CROSSING OF NON-RANDOM FUNCTIONS TO BOUNDARY CROSSING OF STOCHASTIC PROCESSES

2015 ◽  
Vol 29 (3) ◽  
pp. 345-359 ◽  
Author(s):  
Mark Brown ◽  
Victor de la Peña ◽  
Tony Sit
Keyword(s):  
Stochastic Processes ◽  
Sequential Analysis ◽  
Form Solution ◽  
Boundary Crossing ◽  
Renewal Processes ◽  
Bessel Processes ◽  
Average Behavior ◽  
Random Functions ◽  
Close Form ◽  
Sharp Lower Bound

One problem of wide interest involves estimating expected crossing-times. Several tools have been developed to solve this problem beginning with the works of Wald and the theory of sequential analysis. Deriving the explicit close form solution for the expected crossing times may be difficult. In this paper, we provide a framework that can be used to estimate expected crossing times of arbitrary stochastic processes. Our key assumption is the knowledge of the average behavior of the supremum of the process. Our results include a universal sharp lower bound on the expected crossing times. Furthermore, for a wide class of time-homogeneous, Markov processes, including Bessel processes, we are able to derive an upper bound E[a(Tr)]≤2r, which implies that sup r>0|((E[a(Tr)]−r)/r)|≤1, where a(t)=E[sup tXt] with {Xt}t≥0 be a non-negative, measurable process. This inequality motivates our claim that a(t) can be viewed as a natural clock for all such processes. The cases of multidimensional processes, non-symmetric and random boundaries are handled as well. We also present applications of these bounds on renewal processes in Example 10 and other stochastic processes.

scholarly journals On an approach to boundary crossing by stochastic processes

2016 ◽  
Vol 126 (12) ◽  
pp. 3843-3853 ◽  
Author(s):  
Mark Brown ◽  
Victor H. de la Peña ◽  
Michael J. Klass ◽  
Tony Sit
Keyword(s):  
Stochastic Processes ◽  
Boundary Crossing

A New Close-Form Solution for Initial Registration of ICP

2010 ◽  
Vol 143-144 ◽  
pp. 287-292
Author(s):  
Li Zhao Liu ◽  
Xiao Jing Hu ◽  
Yu Feng Chen ◽  
Tian Hua Zhang ◽  
Mao Qing Li
Keyword(s):  
Closed Form Solution ◽  
Goal Function ◽  
Form Solution ◽  
Initial Value ◽  
Global Goal ◽  
Online Matching ◽  
Testing Algorithm ◽  
Close Form ◽  
Eigenvalue And Eigenvector ◽  
The Relationship

The paper proposed a original matching algorithm using the feature vectors of rigid points sets matrix and a online matching intersection testing algorithm using the bounding sphere. The relationship searching between points in each set is took place by the corresponding eigenvectors that is a closed form solution relatively. The affine transformed eigenvalue and eigenvector is also used instead of the affine transformed points sets for the non-rigid matching that do not need the complicated global goal function. The characteristics matching for the initial registration can give a well initial value for the surfaces align that improve the probability of global solution for the following-up ICP

Stress Distribution in and Around Spheroidal Inclusions and Voids at Finite Concentration

1986 ◽  
Vol 53 (3) ◽  
pp. 511-518 ◽  
Author(s):  
G. P. Tandon ◽  
G. J. Weng
Keyword(s):  
Stress Distribution ◽  
Energy Distribution ◽  
Uniaxial Tension ◽  
Elastic Stress ◽  
Three Dimensional ◽  
Tensile Loading ◽  
Form Solution ◽  
Finite Concentration ◽  
The Matrix ◽  
Close Form

A simple, albeit approximate, close-form solution is developed to study the elastic stress and energy distribution in and around spheroidal inclusions and voids at finite concentration. This theory combines Eshelby’s solution of an ellipsoidal inclusion and Mori- Tanaka’s concept of average stress in the matrix. The inclusions are taken to be homogeneously dispersed and undirectionally aligned. The analytical results are obtained for the general three-dimensional loading, and further simplified for uniaxial tension applied parallel to the axis of inclusions. The ensuing stress and energy fields under tensile loading are illustrated for both hard inclusions and voids, ranging from prolate to oblate shapes, at several concentrations.

Streaming Potential Induced by Canaliculi Fluid Flow: A Fluid-Filled Thick-Walled Cylinder Osteon Model Subjected to Axial Loading

2010 ◽  
Vol 34-35 ◽  
pp. 117-122
Author(s):  
Xiao Gang Wu ◽  
Wei Yi Chen
Keyword(s):  
Fluid Flow ◽  
Streaming Potential ◽  
Axial Loading ◽  
Fluid Phase ◽  
Form Solution ◽  
Solid Matrix ◽  
Intraosseous Pressure ◽  
Elastic Transverse ◽  
Close Form ◽  
Walled Cylinder

Based on the physiological structure of osteon, a single fluid-filled osteon model under only time-dependent axial loading is modeled for calculating the streaming potential induced by canaliculi fluid flow. Solid matrix is modeled as an elastic transverse isotropic thick-walled cylinder and fluid phase is considered as an incompressible Newtonian fluid. Close-form solution of the streaming potential for a single osteon model was obtained and used to study the electromechanical properties on intraosseous pressure and potential distribution. The solution can also be used as a benchmark for numerical studies of other osteon models.

Invariance principles in queueing theory

1989 ◽  
Vol 26 (04) ◽  
pp. 845-857
Author(s):  
Michael Alex ◽  
Josef Steinebach
Keyword(s):  
Convergence Rate ◽  
Stochastic Processes ◽  
Queueing Theory ◽  
Counting Process ◽  
Heavy Traffic ◽  
Renewal Processes ◽  
Light Traffic ◽  
Invariance Principles ◽  
Renewal Counting Process ◽  
Compound Renewal Processes

Several stochastic processes in queueing theory are based upon compound renewal processes . For queues in light traffic, however, the summands {Xk }and the renewal counting process {N(t)} are typically dependent on each other. Making use of recent invariance principles for such situations, we present some weak and strong approximations for the GI/G/1 queues in light and heavy traffic. Some applications are discussed including convergence rate statements or Darling–Erdös-type extreme value theorems for the processes under consideration.

Markov processes for modeling and analyzing a new genetic mapping method

1993 ◽  
Vol 30 (04) ◽  
pp. 766-779 ◽  
Author(s):  
Eleanor Feingold
Keyword(s):  
Markov Chains ◽  
Genetic Mapping ◽  
Stochastic Processes ◽  
Markov Processes ◽  
Mapping Method ◽  
Central Issue ◽  
Boundary Crossing ◽  
Crossing Probabilities

This paper describes a set of stochastic processes that is useful for modeling and analyzing a new genetic mapping method. Some of the processes are Markov chains, and some are best described as functions of Markov chains. The central issue is boundary-crossing probabilities, which correspond to p-values for the existence of genes for particular traits. The methods elaborated by Aldous (1989) provide very accurate approximate p-values, as spot-checked against simulations.

Leg kinematic analysis and prototype experiments of walking-operating multifunctional hexapod robot

2013 ◽  
Vol 228 (12) ◽  
pp. 2217-2232 ◽  
Author(s):  
Pan Yang ◽  
Feng Gao
Keyword(s):  
Kinematic Analysis ◽  
Kinematic Model ◽  
Form Solution ◽  
Spherical Joint ◽  
Universal Joint ◽  
Step Size ◽  
Work Space ◽  
Prismatic Joint ◽  
Forward Kinematic ◽  
Close Form

This paper presents kinematic analysis of a 3-degree of freedom parallel mechanism for hexapod walking-operating multifuctional robot. Each leg of the robot consists of three limbs: universal joint – prismatic joint chain (1-UP) and universal joint – prismatic joint – spherical joint chain (2-UPS) and at the end of the leg there is passive spherical joint to adjust to the uneven ground. In this paper, first the forward kinematic model is built and it shows that the model has close-form solution. Then the work space is discussed in which the robot feet trajectories can be projected. It can be shown that the current trajectories of the feet only take very small work space. After that force analysis is performed and the results show that the payload capability of the mechanism is very high. Experiments of the prototype show that the robot can walk easily with more than 150 kg loads while the step size is more than 0.5 m.

scholarly journals TWO MODELS OF NONSMOOTH DYNAMICAL SYSTEMS

2011 ◽  
Vol 21 (10) ◽  
pp. 2853-2860 ◽  
Author(s):  
MADELEINE PASCAL
Keyword(s):  
Dry Friction ◽  
Coupled Oscillators ◽  
Degrees Of Freedom ◽  
Analytical Form ◽  
Critical Value ◽  
Form Solution ◽  
Nonsmooth Systems ◽  
The Stability ◽  
Close Form ◽  
Nonsmooth Dynamical Systems

Two examples of nonsmooth systems are considered. The first one is a two degrees of freedom oscillator in the presence of a stop. A discontinuity appears when the system position reaches a critical value. The second example consists of coupled oscillators excited by dry friction. In this case, the discontinuity occurs when the system's velocities take a critical value. For both examples, the dynamical system can be partitioned into different configurations limited by a set of boundaries. Within each configuration, the dynamical model is linear and the close form solution is known. Periodic orbits, including several transitions between the various configurations of the system, are found in analytical form. The stability of these orbits is investigated by using the Poincaré map modeling.

Moments of age and remaining life in renewal processes

1973 ◽  
Vol 10 (02) ◽  
pp. 307-316
Author(s):  
S. Katz ◽  
P. Naor ◽  
R. Shinnar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Statistical Mechanics ◽  
Sequential Analysis ◽  
Renewal Theory ◽  
Independent Interest ◽  
Renewal Processes ◽  
Remaining Life ◽  
Analysis Framework ◽  
Partial Differential

Expressions are developed for the moments of age and remaining life in renewal processes, and from them, expressions for the moments of the last and next renewal epochs. The results for remaining life and next renewal epoch may be regarded as generalizations of theorems of Wald (1944) and others. The results for age and last renewal epoch do not fit into this sequential analysis framework. Both sets of results are obtained from partial differential equations developed for the distributions of age and of remaining life. These partial differential equations are of the “conservation” type familiar from statistical mechanics, and may have some independent interest for renewal theory.

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