ON THE HITTING PROBABILITY AND POLARITY FOR A CLASS OF SELF-SIMILAR MARKOV PROCESSES

The anthem investigate the hitting probability, polarity and the relationship between the polarity and Hausdorff dimension for self-similar Markov processes with state space (0, infinity) and increasing path.

HITTING PROBABILITIES AND INTERSECTIONS OF TIME-SPACE ANISOTROPIC RANDOM FIELDS

Let X^(H)={X^(H)(s),s∈R^(N_(1))}and X^(K)={X^(K)(t),t∈R^(N_(2))}be two independent time-space anisotropic random fields with indices H∈(0,1)^(N_(1)) and K∈(0,1)^(N_(2)),which may not possess Gaussianity,and which take values in R^(d) with a space metric τ.Under certain general conditions with density functions defined on a bounded interval,we study problems regarding the hitting probabilities of time-space anisotropic random fields and the existence of intersections of the sample paths of random fields X^(H) and X^(K).More generally,for any Borel set F⊂R^(d),the conditions required for F to contain intersection points of X^(H) and X^(K) are established.As an application,we give an example of an anisotropic non-Gaussian random field to show that these results are applicable to the solutions of non-linear systems of stochastic fractional heat equations.

Quantitative method for calculating spatial release region for laser-guided bomb

The laser-guided bomb(LGB)is an air-to-ground pre-cision-guided weapon that offers high hit rates,great power,and ease of use.LGBs are guided by semi-active laser ground-seek-ing technology,which means that atmospheric conditions can affect their accuracy.The spatial release region(SRR)of LGBs is difficult to calculate precisely,especially when there is a poor field of view.This can result in a lower real hit probability.To increase the hit probability of LGBs in tough atmospheric situa-tions,a novel method for calculating the SRR has been pro-posed.This method is based on the transmittance model of the 1.06μm laser in atmospheric species and the laser diffuse reflection model of the target surface to determine the capture target time of the laser seeker.Then,it calculates the boundary ballistic space starting position by ballistic model and gets the spatial scope of the spatial release region.This method can determine the release region of LGBs based on flight test data such as instantaneous velocity,altitude,off-axis angle,and atmospheric visibility.By more effectively employing aircraft release conditions,atmospheric visibility and other factors,the SRR calculation method can improve LGB hit probabi-lity by 9.2%.

Effects of Wind on Steady-state Scan Characteristics and Hit Probability of Terminal-sensitive Projectile

The wind effects on steady-state scan characteristics and hit probability of terminal-sensitive projectile were discussed in this paper. Considering wind as the constitutions of the average wind and the impulsive wind, a simplified wind field model was established for the ballistic calculation of the steady-state scan phase; under the windy condition, the effects of the range wind and the beam wind on the steady-state scan characteristics of the terminal-sensitive projectile were analyzed in detail and its hit probabilities for a certain armored target were calculated. The calculated results show that, when the wind speed exceeds a certain value, the hit probabilities of terminal-sensitive projectile drop rapidly; the wind effects must be considered in the application of the terminal-sensitive projectiles. This paper provides some theoretical references for the fire wind speed correction and the global structure optimization of the terminal-sensitive projectile.

HITTING PROBABILITIES OF WEIGHTED POISSON PROCESSES WITH DIFFERENT INTENSITIES AND THEIR SUBORDINATIONS

In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.

ON INTERSECTIONS OF INDEPENDENT NONDEGENERATE DIFFUSION PROCESSES

Let X（1） = {X（1）（s）, s ∈ R＋} and X（2） = {X（2）（t）, t ∈ R＋} be two inde-pendent nondegenerate diffusion processes with values in Rd. The existence and fractal dimension of intersections of the sample paths of X （1） and X （2） are studied. More gener-ally, let E1, E2？（0,∞） and F ？Rd be Borel sets. A necessary condition and a suffcient condition for P{X（1）（E1）∩X（2）（E2）∩F 6=？}〉0 are proved in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 × E2 × F in the metric space （R＋× R＋× Rd,ρb）, whereρb is an unsymmetric metric defined in R＋× R＋× Rd. Under reasonable conditions, results resembling those of Browian motion are obtained.

FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES

This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity.

Application of Large-Scale Systems Theory in Fire Control Systems

According the to the model of single tank fire control system, this paper makes use of decomposition-coordination theory of large-scale systems to discuss the shooting problem of multiple tank the control systems, and alalyzes specifically the three-tank the control systems and models.the process was imitated in computer, and the optimal shooting element of 3TS system was got. In addition, probability of hitting the target was calculated.

Hitting Probabilities and Fractal Dimensions of Multiparameter Multifractional Brownian Motion

The main goal of this paper is to study the sample path properties for the harmonisable-type N-parameter multifractional Brownian motion, whose local regularities change as time evolves. We provide the upper and lower bounds on the hitting probabilities of an （N, d）-multifractional Brownian motion. Moreover, we determine the Hausdorff dimension of its inverse images, and the Hausdorff and packing dimensions of its level sets.

Hitting Probabilities and the Hausdorff Dimension of the Inverse Images of a Class of Anisotropic Random Fields

Let X = {X（t）：t ∈ R^N} be an anisotropic random field with values in R^d.Under certain conditions on X,we establish upper and lower bounds on the hitting probabilities of X in terms of respectively Hausdorff measure and Bessel-Riesz capacity.We also obtain the Hausdorff dimension of its inverse image,and the Hausdorff and packing dimensions of its level sets.These results are applicable to non-linear solutions of stochastic heat equations driven by a white in time and spatially homogeneous Gaussian noise and anisotropic Guassian random fields.

On intersections of independent anisotropic Gaussian random fields

Let X^H = {X^H（8）,8∈ R^N1} and XK = {X^K（t）,t ∈R^2} be two independent anisotropic Gaussian random fields with values in R^d with indices H = （H1,... ,HN1） ∈ （0, 1）^N1, K = （K1,..., KN2）∈ （0, 1）^N2, respectively. Existence of intersections of the sample paths of XH and XK is studied. More generally, let E1 R^N1, E2 R^N2 and F R^d be Borel sets. A necessary condition and a sufficient condition for P{（X^H（E1） ∩ X^K（E2）） ∩ F ≠ Ф} 〉 0 in terms of the Bessel-Riesz type capacity and Hausdorff measure of E1 x E2 x F in the metric space （R^N1＋N2＋d, ρ） are proved, whereρ is a metric defined in terms of H and K. These results are applicable to solutions of stochastic heat equations driven by space-time Gaussian noise and fractional Brownian sheets.