Vol. 6 No. 2 (2022): Vol 6, Iss 2, Year 2022
Articles

A study on analytical solutions for stochastic differential equations via martingale processes

Syed Tahir Hussainy
Department of Mathematics, Islamiah College (Autonomous), Vaniyambadi 635 752, Tirupattur District, Tamil Nadu India.
Pathmanaban K
Department of Mathematics, Islamiah College (Autonomous), Vaniyambadi 635 752, Tirupattur District, Tamil Nadu India
Published December 7, 2022
Keywords
  • Martingale process Itô formula Change of variable Differentiable process Analytical solution
How to Cite
Syed Tahir Hussainy, & K, P. (2022). A study on analytical solutions for stochastic differential equations via martingale processes. Journal of Computational Mathematica, 6(2), 85 - 92. https://doi.org/10.26524/cm151

Abstract

In this paper, we propose some analytical solutions of stochastic differential equations related to Martingale processes. In the first resolution, the answers of some stochastic differential equations are connected to other stochastic equations just with diffusion part (or drift free). The second suitable method is to convert stochastic differential equations into ordinary ones that it is tried to omit diffusion part of stochastic equation by applying Martingale processes. Finally, solution focuses on change of variable method that can be utilized about stochastic differential equations which are as function of Martingale processes like Wiener process, exponential Martingale process and differentiable processes.

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