Lp solutions of general time interval BSDEs with generators satisfying a p-order weak stochastic-monotonicity condition

2021 ◽  
pp. 1-27
Author(s):  
Xinying Li ◽  
Shengjun Fan
Keyword(s):  
Monotonicity Condition ◽  
Time Interval ◽  
Stochastic Monotonicity ◽  
Lp Solutions ◽  
General Time

scholarly journals General time interval multidimensional BSDEs with generators satisfying a weak stochastic-monotonicity condition

2021 ◽  
Vol 6 (4) ◽  
pp. 301
Author(s):  
Tingting Li ◽  
Ziheng Xu ◽  
Shengjun Fan
Keyword(s):  
Backward Stochastic Differential Equation ◽  
Type Inequality ◽  
Uniqueness Result ◽  
The State ◽  
Monotonicity Condition ◽  
Time Interval ◽  
Stochastic Monotonicity ◽  
State Variable ◽  
Martingale Representation Theorem ◽  
General Time

<p style='text-indent:20px;'>This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator <inline-formula> <tex-math id="M1">\begin{document}$ g $\end{document}</tex-math> </inline-formula> satisfies a weak stochastic-monotonicity condition and a general growth condition in the state variable <inline-formula> <tex-math id="M2">\begin{document}$ y $\end{document}</tex-math> </inline-formula>, and a stochastic-Lipschitz condition in the state variable <inline-formula> <tex-math id="M3">\begin{document}$ z $\end{document}</tex-math> </inline-formula>. This unifies and strengthens some known works. In order to prove this result, we develop some ideas and techniques employed in Xiao and Fan [<xref ref-type="bibr" rid="b25">25</xref>] and Liu et al. [<xref ref-type="bibr" rid="b15">15</xref>]. In particular, we put forward and prove a stochastic Gronwall-type inequality and a stochastic Bihari-type inequality, which generalize the classical ones and may be useful in other applications. The martingale representation theorem, Itô’s formula, and the BMO martingale tool are used to prove these two inequalities. </p>

scholarly journals Lp (p ≥ 1) solutions of multidimensional BSDEs with monotone generators in general time intervals

2014 ◽  
Vol 15 (01) ◽  
pp. 1550002 ◽  
Author(s):  
Li-Shun Xiao ◽  
Sheng-Jun Fan ◽  
Na Xu
Keyword(s):  
Differential Equation ◽  
Weak Convergence ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Additional Assumption ◽  
Backward Stochastic Differential Equation ◽  
Time Interval ◽  
Time Intervals ◽  
Lipschitz Continuous ◽  
General Time

In this paper, we are interested in solving general time interval multidimensional backward stochastic differential equation in Lp (p ≥ 1). We first study the existence and uniqueness for Lp (p > 1) solutions by the method of convolution and weak convergence when the generator is monotonic in y and Lipschitz continuous in z both non-uniformly with respect to t. Then we obtain the existence and uniqueness for L1 solutions with an additional assumption that the generator has a sublinear growth in z non-uniformly with respect to t.

Stochastic monotonicity properties of multiserver queues with impatient customers

1991 ◽  
Vol 28 (03) ◽  
pp. 673-682
Author(s):  
Partha P. Bhattachary ◽  
Anthony Ephremides
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Time Interval ◽  
Impatient Customers ◽  
Monotone Functions ◽  
Stochastic Monotonicity ◽  
Multiserver Queues ◽  
Monotonicity Properties ◽  
Number Of Customers

We consider multiserver queues in which a customer is lost whenever its waiting time is larger than its (possibly random) deadline. For such systems, the number of (successful) departures and the number of customers lost over a time interval are the performance measures of interest. We show that these quantities are (stochastically) monotone functions of the arrival, service and deadline processes.

Bounded solutions for general time interval BSDEs with quadratic growth coefficients and stochastic conditions

2018 ◽  
Vol 18 (05) ◽  
pp. 1850034
Author(s):  
Huan-Huan Luo ◽  
Sheng-Jun Fan
Keyword(s):  
Differential Equations ◽  
Finite Time ◽  
Quadratic Growth ◽  
Time Interval ◽  
Finite Time Interval ◽  
Bounded Solutions ◽  
One Dimensional ◽  
Stochastic Conditions ◽  
New Ideas ◽  
General Time

This paper deals with bounded solutions for general time interval one-dimensional backward stochastic differential equations (BSDEs for short) with quadratic growth coefficients and stochastic conditions. Several general results of existence, uniqueness, stability and comparison for the bounded solutions are put forward and established, which improve considerably some existing works, even though for the case of finite time interval. Some new ideas are also developed to establish these results.

Stochastic monotonicity properties of multiserver queues with impatient customers

1991 ◽  
Vol 28 (3) ◽  
pp. 673-682 ◽  
Author(s):  
Partha P. Bhattacharya ◽  
Anthony Ephremides
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Time Interval ◽  
Impatient Customers ◽  
Monotone Functions ◽  
Stochastic Monotonicity ◽  
Multiserver Queues ◽  
Monotonicity Properties ◽  
Number Of Customers

We consider multiserver queues in which a customer is lost whenever its waiting time is larger than its (possibly random) deadline. For such systems, the number of (successful) departures and the number of customers lost over a time interval are the performance measures of interest. We show that these quantities are (stochastically) monotone functions of the arrival, service and deadline processes.

scholarly journals Backward stochastic differential equations with stochastic monotone coefficients

2004 ◽  
Vol 2004 (4) ◽  
pp. 317-335 ◽  
Author(s):  
K. Bahlali ◽  
A. Elouaflin ◽  
M. N'zi
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Existence And Uniqueness ◽  
Backward Stochastic Differential Equations ◽  
Uniqueness Result ◽  
Nonlinear Pdes ◽  
Monotonicity Condition ◽  
Stochastic Monotonicity ◽  
Monotone Coefficients ◽  
Terminal Time

We prove an existence and uniqueness result for backward stochastic differential equations whose coefficients satisfy a stochastic monotonicity condition. In this setting, we deal with both constant and random terminal times. In the random case, the terminal time is allowed to take infinite values. But in a Markovian framework, that is coupled with a forward SDE, our result provides a probabilistic interpretation of solutions to nonlinear PDEs.

scholarly journals Lp solutions of infinite time interval backward doubly stochastic differential equations

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1857-1868 ◽  
Author(s):  
Zhaojun Zong ◽  
Feng Hu
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Uniqueness Theorem ◽  
Existence And Uniqueness ◽  
Time Interval ◽  
Existence And Uniqueness Theorem ◽  
Infinite Time ◽  
Doubly Stochastic ◽  
Infinite Time Interval ◽  
Lp Solutions

In this paper, we study the existence and uniqueness theorem for Lp (1 < p < 2) solutions to a class of infinite time interval backward doubly stochastic differential equations (BDSDEs). Furthermore, we obtain the comparison theorem for 1-dimensional infinite time interval BDSDEs in Lp.

Focusing of Visuospatial Attention

2001 ◽  
Vol 15 (4) ◽  
pp. 256-274 ◽  
Author(s):  
Caterina Pesce ◽  
Rainer Bösel
Keyword(s):  
Reaction Times ◽  
Visual Space ◽  
Spatial Relation ◽  
Stimulus Onset ◽  
Visuospatial Attention ◽  
Task Demands ◽  
Time Interval ◽  
Behavioral Studies ◽  
Task Conditions ◽  
Simple Rt

Abstract In the present study we explored the focusing of visuospatial attention in subjects practicing and not practicing activities with high attentional demands. Similar to the studies of Castiello and Umiltà (e. g., 1990) , our experimental procedure was a variation of Posner's (1980) basic paradigm for exploring covert orienting of visuospatial attention. In a simple RT-task, a peripheral cue of varying size was presented unilaterally or bilaterally from a central fixation point and followed by a target at different stimulus-onset-asynchronies (SOAs). The target could occur validly inside the cue or invalidly outside the cue with varying spatial relation to its boundary. Event-related brain potentials (ERPs) and reaction times (RTs) were recorded to target stimuli under the different task conditions. RT and ERP findings showed converging aspects as well as dissociations. Electrophysiological results revealed an amplitude modulation of the ERPs in the early and late Nd time interval at both anterior and posterior scalp sites, which seems to be related to the effects of peripheral informative cues as well as to the attentional expertise. Results were: (1) shorter latency effects confirm the positive-going amplitude enhancement elicited by unilateral peripheral cues and strengthen the criticism against the neutrality of spatially nonpredictive peripheral cueing of all possible target locations which is often presumed in behavioral studies. (2) Longer latency effects show that subjects with attentional expertise modulate the distribution of the attentional resources in the visual space differently than nonexperienced subjects. Skilled practice may lead to minimizing attentional costs by automatizing the use of a span of attention that is adapted to the most frequent task demands and endogenously increases the allocation of resources to cope with less usual attending conditions.

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