Faster Than Sound, Daredevil Parachute Jumps from the Edge of the Space

This article discusses the kinematics of a parachutist making a very-high-altitude jump. The effect of altitude on the density of air, on the gravitational field strength of the Earth, and on the atmosphere’s temperature has been taken into account in our analysis. The well-known equations of classical mechanics governing the selected topic have been solved numerically by using the mathematical software Mathcad. Especially, the possibility of a person exceeding the speed of sound during their fall has been considered in our analysis. The effect of the sound barrier is taken into account so that the shape factor of the falling body is given as a speed-dependent function, which reaches its maximum value at Mach 1.0. The obtained results have been found to be highly consistent with the available experimental data on some high-altitude jumps. The data published on the famous jump of Captain Joseph Kittinger has been analyzed very carefully, and although our calculations reproduced the reported values for most parts, some interesting inconsistencies were also discovered. Kittinger jumped from a gondola attached to a helium-filled balloon from a record-high altitude of 102,800 ft, or 31,330 m, in August 1960. We also made numerical analysis on the high-altitude jump of Felix Baumgartner. He bailed out from his gondola at the record-high altitude of 39.0 km in October 2012.

The two annual northward jumps of the West Pacific Subtropical High and their relationship with summer rainfall in Eastern China under global warming

The two northward jumps of summer West Pacific Subtropical High （WPSH） are defined based on the pentad-scale ridge data of the WPSH ridge in 1951 to 2012. The times of the northward jumps are found to have obvious inter-annual and decadal characteristics, i.e., the occurrence of the first northward jump of WPSH shows a ＂consistently early-consistently late＂ decadal pattern, with the transition around 1980; the occurrence of the second northward jump of WPSH shows a ＂consistently late-consistently early-consistently late＂ decadal pattern, with the transitions about 1955 and 1978, respec- tively, which is consistent with global warming. In the meantime, the times of the two northward jumps not only have a good correspondence to the beginning and ending dates of the rainy season, but also greatly influence the position of the main rain belt in Eastern China. When the first northward jump occurs early, the main rain belt is located from just north of 30~ N to the south of North China, while the opposite situation appears when the first jump occurs late. When the second jump occurs early, more rain falls over North China and South China, but less falls in the Yangtze River region, while the opposite situation appears when the second jump occurs late. In the four cases when abnormalities occur in the same year as early or late northward jumps, the position of the main rain belt can be considered as a superposition of isolated abnormal effects of the two northward jumps. Moreover, the prophase and synchronous forces of the sea surface temperature in the Pacific has great influence on the times of the northward jumps, and the driving forces of the two jumps differ.

Approximate Controllability of Second-Order Neutral Stochastic Differential Equations with Infinite Delay and Poisson Jumps

The modelling of risky asset by stochastic processes with continuous paths, based on Brow- nian motions, suffers from several defects. First, the path continuity assumption does not seem reason- able in view of the possibility of sudden price variations （jumps） resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.

WAVELET ESTIMATION FOR JUMPS IN A HETEROSCEDASTIC REGRESSION MODEL

Wavelets are applied to detect the jumps in a heteroscedastic regression model. It is shown that the wavelet coefficients of the data have significantly large absolute values across fine scale levels near the jump points. Then a procedure is developed to estimate the jumps and jump heights. All estimators are proved to be consistent.

An Energy-Efficient Protocol Using an Objective Function & Random Search with Jumps forWSN

Wireless Sensor Networks(WSNs)have hardware and software limitations and are deployed in hostile environments.The problem of energy consumption in WSNs has become a very important axis of research.To obtain good performance in terms of the network lifetime,several routing protocols have been proposed in the literature.Hierarchical routing is considered to be the most favorable approach in terms of energy efficiency.It is based on the concept parent-child hierarchy where the child nodes forward their messages to their parent,and then the parent node forwards them,directly or via other parent nodes,to the base station(sink).In this paper,we present a new Energy-Efficient clustering protocol for WSNs using an Objective Function and Random Search with Jumps(EEOFRSJ)in order to reduce sensor energy consumption.First,the objective function is used to find an optimal cluster formation taking into account the ratio of the mean Euclidean distance of the nodes to their associated cluster heads(CH)and their residual energy.Then,we find the best path to transmit data from the CHs nodes to the base station(BS)using a random search with jumps.We simulated our proposed approach compared with the Energy-Efficient in WSNs using Fuzzy C-Means clustering(EEFCM)protocol using Matlab Simulink.Simulation results have shown that our proposed protocol excels regarding energy consumption,resulting in network lifetime extension.

Infinite Horizon LQ Zero-Sum Stochastic Differential Games with Markovian Jumps

This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’s differential equation with state-dependent noise and Markovian parameter jumps. Under the assumption of stochastic stabilizability, necessary and sufficient condition for the existence of the optimal control strategies is presented by means of a system of coupled algebraic Riccati equations via using the stochastic optimal control theory. Furthermore, the stochastic H∞ control problem for stochastic systems with Markovian jumps is discussed as an immediate application, and meanwhile, an illustrative example is presented.

ON SOLUTIONS OF BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS WITH JUMPS,WITH UNBOUNDED STOPPING TIMES AS TERMINAL AND WITH NON-LIPSCHITZ COEFFICIENTS,AND PROBABILISTIC INTERPRETATION OF QUASI-LINEAR ELLIPTIC TYPE INTEGRO-DIFFERENTIAL EQUATIO

The existence and uniqueness of solutions to backward stochastic differential equations with jumps and with unbounded stopping time as terminal under the non_Lipschitz condition are obtained. The convergence of solutions and the continuous dependence of solutions on parameters are also derived. Then the probabilistic interpretation of solutions to some kinds of quasi_linear elliptic type integro_differential equations is obtained.

Two-Sided First Exit Problem for Jump Diffusion Distribution Processes Having Jumps with a Mixture of Erlang

In this paper, we consider the two-sided first exit problem for jump diffusion processes having jumps with rational Laplace transforms. We investigate the probabilistic property of conditional memorylessness, and drive the joint distribution of the first exit time from an interval and the overshoot over the boundary at the exit time.

On necessity proof of strict bounded real lemma for generalized linear systems with finite discrete jumps

Some preliminary results on strict bounded real lemma for time-varying continuous linear systems are proposed, where uncertainty in initial conditions, terminal cost and extreme of the cost function are dealt with explicitly. Based on these results, a new recursive approach is proposed in the necessity proof of strict bounded real lemma for generalized linear system with finite discrete jumps.

Freidlin-Wentzell’s Large Deviations for Stochastic Evolution Equations with Poisson Jumps

We establish a Freidlin-Wentzell’s large deviation principle for general stochastic evolution equations with Poisson jumps and small multiplicative noises by using weak convergence method.

REFLECTED BACKWARD STOCHASTIC DIFFERENTIAL EQUATION WITH JUMPS AND VISCOSITY SOLUTION OF SECOND ORDER INTEGRO-DIFFERENTIAL EQUATION WITHOUT MONOTONICITY CONDITION: CASE WITH THE MEASURE OF LéVY INFINITE

We consider the problem of viscosity solution of integro-partial differential equation( IPDE in short) with one obstacle via the solution of reflected backward stochastic dif ferential equations(RBSDE in short) with jumps. We show the existence and uniqueness of a continuous viscosity solution of equation with non local terms, if the generator is not monotonous and Levy's measure is infinite.

Spillovers among China’s precious and industrial metals markets:Evidence from higher moments and jumps

This study reveals the time-varying spillover effects of higher moments(realized volatility,realized skewness and realized kurtosis)and jumps between China’s precious metals and industrial metals markets.Using 5-min high-frequency data from May 10,2012 to October 21,2021,the dynamic effects of spillovers are uncovered using the time-frequency domain spillover index framework.The results show that the system connectedness weakens as the moment order gets higher whereas the total jumps connectedness is the smallest,and the spillovers of all estimators are more evident in the short term.The overall information spillovers are time-varying and influenced by major market events.Specifically,for realized volatility,copper is the largest net transmitter and silver is always a net transmitter,while zinc is the largest net receiver.For realized skewness,copper is the largest net transmitter and silver is always a net transmitter,while lead is the largest net receiver.For realized kurtosis and jumps,copper is the largest net transmitter,while aluminum is the largest net receiver.Overall,copper and silver play dominant roles in China’s precious and industrial metals markets system.

A NOTE ON STOCHASTIC OPTIMAL CONTROL OF REFLECTED DIFFUSIONS WITH JUMPS

Stochastic optimal control problems for a class of reflected diffusion with Poisson jumps in a half-space are considered. The nonlinear Nisio' s semigroup for such optimal control problems was constructed. A Hamilton-Jacobi-Bellman equation with the Neumann boundary condition associated with this semigroup was obtained. Then, viscosity solutions of this equation were defined and discussed, and various uniqueness of this equation was also considered. Finally, the value function was such optimal control problems is shown to be a viscosity solution of this equation.

Pricing VIX options in a 3/2 plus jumps model

This paper proposes and makes a study of a new model(called the 3/2 plus jumps model) for VIX option pricing. The model allows the mean-reversion speed and volatility of volatility to be highly sensitive to the actual level of VIX. In particular, the positive volatility skew is addressed by the 3/2 plus jumps model. Daily calibration is used to prove that the proposed model preserves its validity and reliability for both in-sample and out-of-sample tests.The results show that the models are capable of fitting the market price while generating positive volatility skew.

Determination of jumps for functions via derivative Gabor series

Recently, Shi Xianliang and Hu Lan published the method of concentration factors for determination of jumps of functions via MCM conjugate wavelets. Usually, it is difficult to calculate the Hilbert transform of general window functions. The aim of this paper is to discuss determination of jumps for functions based on derivative Gabor series. The results will simplify the calculation of jump values.

Pricing VIX options with stochastic skew and asymmetric jumps

This paper performs several empirical exercises to provide evidence that the stochas-tic skew behavior and asymmetric jumps exist in VIX markets.In order to adequately capture all of the features,we develop a general valuation model and obtain quasi-analytical solutions for pricing VIX options.In addition,we make comparative studies of alternative models to illustrate the e ects after taking into account these features on the valuation of VIX options and investigate the relative value of an additional volatility factor and jump components.The empirical results indicate that the multi-factor volatility structure is vital to VIX option pricing due to providing more exibility in the modeling of VIX dynamics,and the need for asymmetric jumps cannot be eliminated by an additional volatility factor.

To jump or not to jump:momentum of jumps in crude oil price volatility prediction

A well-documented finding is that explicitly using jumps cannot efficiently enhance the predictability of crude oil price volatility.To address this issue,we find a phenomenon,“momentum of jumps”(MoJ),that the predictive ability of the jump component is persistent when forecasting the oil futures market volatility.Specifically,we propose a strategy that allows the predictive model to switch between a benchmark model without jumps and an alternative model with a jump component according to their recent past forecasting performance.The volatility data are based on the intraday prices of West Texas Intermediate.Our results indicate that this simple strategy significantly outperforms the individual models and a series of competing strategies such as forecast combinations and shrinkage methods.A mean–variance investor who targets a constant Sharpe ratio can realize the highest economic gains using the MoJ-based volatility forecasts.Our findings survive a wide variety of robustness tests,including different jump measures,alternative volatility measures,various financial markets,and extensive model specifications.

Dynamic Portfolio Choice under Time-Varying,Jumps,and Knight Uncertainty of Asset Return Process

By introducing a stochastic element to the double-jump diffusion framework to measure the Knight uncertainty of asset return process,the model of dynamic portfolio choice was built,which maximized the expected utility of terminal portfolio wealth.Through specifying the state function of uncertainty-aversion,it utilized the max-min method to derive the analytical solution of the model to study the effect of time-varying,jumps,and Knight uncertainty of asset return process on dynamic portfolio choice and their interactions.Results of comparative analysis show:the time-varying results in positive or negative intertemporal hedging demand of portfolio,which depends on the coefficient of investor's risk aversion and the correlation coefficient between return shift and volatility shift;the jumps in asset return overall reduce investor's demand for the risky asset,which can be enhanced or weakened by the jumps in volatility;due to the existing of Knight uncertainty,the investor avoids taking large position on risky asset,and improves portfolio's steady and immunity;the effects of the time-varying,jumps,and Knight uncertainty are interactive.

Exact Quasi-Classical Asymptotic beyond Maslov Canonical Operator and Quantum Jumps Nature

Exact quasi-classical asymptotic beyond WKB-theory and beyond Maslov canonical operator to the Colombeau solutions of the n-dimensional Schrodinger equation is presented. Quantum jumps nature is considered successfully. We pointed out that an explanation of quantum jumps can be found to result from Colombeau solutions of the Schrodinger equation alone without additional postulates.