A closer look at the solutions of a degenerate stochastic differential equation

Authors

  • M.N. Pascu Transilvania University of Brasov, Romania
  • N.R. Pascu Southern Polytechnic State University, USA

Keywords:

degenerate stochastic differential equation, existence and uniqueness, Brownian motion, representation of solution

Abstract

In an attempt to better understand the existence and uniqueness of strong solutions of stochastic differential equations, we study a classical example of a degenerate stochastic differential equation, attributed to H. Tanaka, for which the existence and uniqueness of strong solutions fail, but for which we can explicitly describe the set of all (weak) solutions.

Author Biographies

M.N. Pascu, Transilvania University of Brasov, Romania

Faculty of Mathematics and Computer Science, Str. Iuliu Maniu Nr. 50, Brasov - 500091

N.R. Pascu, Southern Polytechnic State University, USA

Department of Mathematics, 1100 S. Marietta Pkwy, Marietta, GA 30060-2896

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Published

2012-01-10

Issue

Vol. 4(53) No. 2 (2011)

Section

MATHEMATICS