• 제목/요약/키워드: comparison theorem

검색결과 83건 처리시간 0.029초

Lp SOLUTIONS FOR GENERAL TIME INTERVAL MULTIDIMENSIONAL BSDES WITH WEAK MONOTONICITY AND GENERAL GROWTH GENERATORS

  • Dong, Yongpeng;Fan, Shengjun
    • 대한수학회논문집
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    • 제33권3호
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    • pp.985-999
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    • 2018
  • This paper is devoted to the existence and uniqueness of $L^p$ (p > 1) solutions for general time interval multidimensional backward stochastic differential equations (BSDEs for short), where the generator g satisfies a ($p{\wedge}2$)-order weak monotonicity condition in y and a Lipschitz continuity condition in z, both non-uniformly in t. The corresponding stability theorem and comparison theorem are also proved.

THE SOLUTIONS OF BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS WITH NON-LIPSCHITZ COEFFICIENTS

  • Han, Baoyan;Zhu, Bo
    • Journal of applied mathematics & informatics
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    • 제29권5_6호
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    • pp.1143-1155
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    • 2011
  • In this paper, we shall establish a new theorem on the existence and uniqueness of the solution to a backward doubly stochastic differential equations under a weaker condition than the Lipschitz coefficient. We also show a comparison theorem for this kind of equations.

MEAN-FIELD BACKWARD STOCHASTIC DIFFERENTIAL EQUATIONS ON MARKOV CHAINS

  • Lu, Wen;Ren, Yong
    • 대한수학회보
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    • 제54권1호
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    • pp.17-28
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    • 2017
  • In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.

COMPARISON FOR SOLUTIONS OF A SPDE DRIVEN BY MARTINGALE MEASURE

  • CHO, NHAN-SOOK
    • 대한수학회보
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    • 제42권2호
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    • pp.231-244
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    • 2005
  • We derive a comparison theorem for solutions of the following stochastic partial differential equations in a Hilbert space H. $$Lu^i=\alpha(u^i)M(t,\; x)+\beta^i(u^i),\;for\;i=1,\;2,$$ $where\;Lu^i=\;\frac{\partial u^i}{\partial t}\;-\;Au^{i}$, A is a linear closed operator on Hand M(t, x) is a spatially homogeneous Gaussian noise with covariance of a certain form. We are going to show that if $\beta^1\leq\beta^2\;then\;u^1{\leq}u^2$ under some conditions.

CONSTRUCTIVE AND DISCRETE VERSIONS OF THE LYAPUNOV′S STABILITY THEOREM AND THE LASALLE′S INVARIANCE THEOREM

  • Lee, Jae-Wook
    • 대한수학회논문집
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    • 제17권1호
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    • pp.155-163
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    • 2002
  • The purpose of this paper is to establish discrete versions of the well-known Lyapunov's stability theorem and LaSalle's invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and continuous dynamical systems is conducted.

OSCILLATION THEOREMS FOR PERTURBED DIFFERENTIAL EQUATIONS OF SECOND ORDER

  • Kim, Rak-Joong
    • 대한수학회보
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    • 제45권2호
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    • pp.241-252
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    • 2008
  • By means of a Riccati transform and averaging technique some oscillation criteria are established for perturbed nonlinear differential equations of second order $(P_1)\;(p(t)x'(t))'+q(t)|x({\phi}(t)|^{{\alpha}+1}sgnx({\phi}(t))+g(t,\;x(t))=0$ $(P_2)$ and $(P_3)$ satisfying the condition (H). A comparison theorem and examples are given.

TAMED EXHAUSTION FUNCTIONS AND SCHWARZ TYPE LEMMAS FOR ALMOST HERMITIAN MANIFOLDS

  • Weike, Yu
    • 대한수학회보
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    • 제59권6호
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    • pp.1423-1438
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    • 2022
  • In this paper, we study a special exhaustion function on almost Hermitian manifolds and establish the existence result by using the Hessian comparison theorem. From the viewpoint of the exhaustion function, we establish a related Schwarz type lemma for almost holomorphic maps between two almost Hermitian manifolds. As corollaries, we deduce several versions of Schwarz and Liouville type theorems for almost holomorphic maps.

COMPARISON EXAMPLES ON GENERALIZED QUASI-VARIATIONAL INEQUALITIES

  • Kum, Sang-Ho
    • 대한수학회보
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    • 제36권2호
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    • pp.371-377
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    • 1999
  • The purpose of this paper is to provide two examples which prove that Cubiotti's theorem and Yao's one on the generalized quasi-variational inequality problem are independent of each other. In addition, we give another example which tells us that certain conditions are essential in Cubiotti's theorem and Yao's one.

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Teaching the Intermediate Value Theorem with Non-Existing Examples

  • Hwang, Jihyun;Hong, Dae S.
    • 한국수학교육학회지시리즈D:수학교육연구
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    • 제23권1호
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    • pp.1-12
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    • 2020
  • In this case study, a professor was observed to investigate use of instructional examples when teaching the Intermediate Value Theorem in a calculus course. Video-recorded lessons were analyzed with constant comparison to video-stimulated recall interviews and field notes. The professor employed multiple instructional examples, which was initiated by students and modified by the professor. The professor asked students to build non-existing examples as an informal proof of the Intermediate Value Theorem and assessment of students' previous knowledge. Use of incorrect examples on instructional purpose can be an appropriate way for formative assessment as well as a bridge between informal and formal proofs in college mathematics.