Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations

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• 作者：Alexander Melnikov (1)
  Yuliya Mishura (2)
  Georgiy Shevchenko (2)
  
  1. Department of Mathematical and Statistical Sciences ; University of Alberta ; 632 Central Academic Building ; Edmonton ; AB ; T6G 2G1 ; Canada
  2. Faculty of Mechanics and Mathematics ; Department of Probability ; Statistics and Actuarial Mathematics ; Kyiv National Taras Shevchenko University ; Volodymyrska 64 ; 01601 ; Kyiv ; Ukraine
  
• 关键词：Mixed stochastic differential equation ; Pathwise integral ; Stochastic viability ; Comparison theorem ; Long ; range dependence ; fractional Brownian motion ; Stochastic differential equation with random drift ; 60G22 ; 60G15 ; 60H10 ; 26A33
• 刊名：Methodology and Computing in Applied Probability
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：17
• 期：1
• 页码：169-188
• 全文大小：501 KB
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• 刊物主题：Statistics, general; Life Sciences, general; Electrical Engineering; Economics general; Business/Management Science, general;
• 出版者：Springer US
• ISSN：1573-7713

文摘

For a mixed stochastic differential equation containing both Wiener process and a H枚lder continuous process with exponent 纬鈥?鈥?/2, we prove a stochastic viability theorem. As a consequence, we get a result about positivity of solution and a pathwise comparison theorem. An application to option price estimation is given.