Stochastic Viability and Comparison Theorems for Mixed Stochastic Differential Equations

Alexander Melnikov (), Yuliya Mishura () and Georgiy Shevchenko ()
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Alexander Melnikov: University of Alberta
Yuliya Mishura: Kyiv National Taras Shevchenko University
Georgiy Shevchenko: Kyiv National Taras Shevchenko University

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 1, 169-188

Abstract: Abstract For a mixed stochastic differential equation containing both Wiener process and a Hölder continuous process with exponent γ > 1/2, 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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11009-013-9336-9

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