Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Limits with Oscillating Discontinuities01:19

Limits with Oscillating Discontinuities

264
An oscillating discontinuity is a type of discontinuity in which a function’s values fluctuate infinitely often as the input approaches a particular point. Unlike jump discontinuities, where the function suddenly shifts between two values, or infinite discontinuities, where the function diverges without bound, an oscillating discontinuity arises from rapid back-and-forth variation. Because the function never stabilizes toward a single value, no finite limit exists at that point.One of the...
264
Classification of Systems-II01:31

Classification of Systems-II

439
Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
439
Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

920
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured from...
920
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

852
System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system....
852
Linear time-invariant Systems01:23

Linear time-invariant Systems

821
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
821
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

301
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
301

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Electrophysiological Characteristics and Ablation Outcomes in Patients With Catecholaminergic Polymorphic Ventricular Tachycardia.

Journal of the American Heart Association·2023
Same author

Favorable response to surufatinib in a patient with necrolytic migratory erythema: A case report.

Open life sciences·2023
Same author

Angioplasty Guidewire-Assisted vs. Conventional Transseptal Puncture for Left Atrial Appendage Occlusion: a multicentre randomized controlled trial.

Europace : European pacing, arrhythmias, and cardiac electrophysiology : journal of the working groups on cardiac pacing, arrhythmias, and cardiac cellular electrophysiology of the European Society of Cardiology·2023
Same author

Central vertical regulation and urban environment-biased technological progress: evidence from China.

Environmental science and pollution research international·2023
Same author

Smart Dual-Exsolved Self-Assembled Anode Enables Efficient and Robust Methane-Fueled Solid Oxide Fuel Cells.

Advanced science (Weinheim, Baden-Wurttemberg, Germany)·2023
Same author

Ambient γ-Rays-Mediated Noble-Metal Deposition on Defect-Rich Manganese Oxide for Glycerol-Assisted H<sub>2</sub> Evolution at Industrial-Level Current Density.

Angewandte Chemie (International ed. in English)·2023

Related Experiment Video

Updated: Jan 3, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

453

Infinite time interval backward stochastic differential equations with continuous coefficients.

Zhaojun Zong1, Feng Hu1

  • 1School of Statistics, Qufu Normal University, Qufu, 273165 China.

Springerplus
|November 1, 2016
PubMed
Summary

This study establishes existence theorems for infinite time interval backward stochastic differential equations (BSDEs) with continuous coefficients and linear growth. A minimal solution is also proven to exist, alongside unique solutions for non-uniformly Lipschitz coefficients.

Keywords:
Backward stochasticComparison theoremDifferential equation (BSDE)Linear growth condition

More Related Videos

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.1K
X-ray Beam Induced Current Measurements for Multi-Modal X-ray Microscopy of Solar Cells
10:16

X-ray Beam Induced Current Measurements for Multi-Modal X-ray Microscopy of Solar Cells

Published on: August 20, 2019

14.3K

Related Experiment Videos

Last Updated: Jan 3, 2026

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

453
Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
06:45

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

Published on: October 28, 2022

2.1K
X-ray Beam Induced Current Measurements for Multi-Modal X-ray Microscopy of Solar Cells
10:16

X-ray Beam Induced Current Measurements for Multi-Modal X-ray Microscopy of Solar Cells

Published on: August 20, 2019

14.3K

Area of Science:

  • Stochastic Analysis
  • Mathematical Finance
  • Partial Differential Equations

Background:

  • Backward Stochastic Differential Equations (BSDEs) are crucial for modeling financial markets and solving partial differential equations.
  • Infinite time interval BSDEs present unique challenges due to their unbounded nature.
  • Existing literature often requires strong conditions on coefficients, limiting applicability.

Purpose of the Study:

  • To investigate the existence of L^p solutions for 1-dimensional infinite time interval BSDEs with continuous coefficients and linear growth.
  • To establish the existence of a minimal solution for these BSDEs.
  • To explore the existence and uniqueness of L^p solutions for BSDEs with non-uniformly Lipschitz coefficients, relaxing existing conditions.

Main Methods:

  • Utilizing fixed-point theorems and analytical techniques to prove existence.
  • Developing novel approaches to handle the infinite time horizon and weaker coefficient conditions.
  • Comparing results with existing theorems to highlight advancements.

Main Results:

  • Existence of L^p solutions for a class of 1D infinite time interval BSDEs with continuous, linearly growing coefficients.
  • Proof of the existence of a minimal solution.
  • Establishment of existence and uniqueness for L^p solutions under non-uniformly Lipschitz conditions, improving upon prior work.

Conclusions:

  • The study expands the theoretical framework for infinite time interval BSDEs.
  • The findings offer more flexible conditions for analyzing these equations.
  • This research contributes to a deeper understanding of stochastic differential equations and their applications.