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COMPARISON FOR SOLUTIONS OF A SPDE DRIVEN BY MARTINGALE MEASURE

CHO, NHAN-SOOK    (HANSUNG UNIVERSITY  );
  • 초록

    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.


  • 주제어

    comparison theorem .   SPDE .   martingale measure.  

  • 참고문헌 (11)

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    4. C. Donald-Martin and E. Pardoux, White noise driven SPDES with reflection, Probab. Theory Related Fields 95 (1993), 1{24 
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 저자의 다른 논문

  • Cho, Nhan-Sook (10)

    1. 1996 "ON A MARTINGALE PROBLEM AND A RELAXED CONTROL PROBLEM W.R.T. SDE" Journal of the Korean Mathematical Society = 대한수학회지 33 (4): 777~791    
    2. 1997 "ON ASYMPTOTIC BEHAVIOR OF A RANDOM EVOLUTION" Bulletin of the Korean Mathematical Society = 대한수학회보 34 (2): 233~245    
    3. 1997 "ON THE SQUARE OF BROWNIAN DENSITY PROCESS" Journal of the Korean Mathematical Society = 대한수학회지 34 (3): 707~717    
    4. 1999 "A LAW OF ITERATED LOGARITHM FOR OCCUPATION TIME BROWNIAN IN ι$_2$" Communications of the Korean Mathematical Society = 대한수학회논문집 14 (3): 569~579    
    5. 2001 "ESTIMATES IN EXIT PROBABILITY FOR SOLUTIONS OF NUCLEAR SPACE-VALUED SDE" Bulletin of the Korean Mathematical Society = 대한수학회보 38 (1): 129~136    
    6. 2002 "ON THE HAUSDORFF MEASURE FOR A TRAJECTORY OF A BROWNIAN MOT10N IN l2" Communications of the Korean Mathematical Society = 대한수학회논문집 17 (1): 81~93    
    7. 2003 "LIMIT OF SOLUTIONS OF A SPDE DRIVEN BY MARTINGALE MEASURE WITH REFLECTION" Communications of the Korean Mathematical Society = 대한수학회논문집 18 (4): 713~723    
    8. 2004 "CENTRAL LIMIT TYPE THEOREM FOR WEIGHTED PARTICLE SYSTEMS" Journal of the Korean Mathematical Society = 대한수학회지 41 (5): 773~793    
    9. 2005 "LARGE DEVIATION PRINCIPLE FOR DIFFUSION PROCESSES IN A CONUCLEAR SPACE" Communications of the Korean Mathematical Society = 대한수학회논문집 20 (2): 381~393    
    10. 2006 "LARGE DEVIATION PRINCIPLE FOR SOLUTIONS TO SDE DRIVEN BY MARTINGALE MEASURE" Communications of the Korean Mathematical Society = 대한수학회논문집 21 (3): 543~558    

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