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Stochastic differential equations for Dirichlet processes
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  • Published: November 2001

Stochastic differential equations for Dirichlet processes

  • Richard F. Bass1 &
  • Zhen-Qing Chens2 

Probability Theory and Related Fields volume 121, pages 422–446 (2001)Cite this article

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Abstract.

We consider the stochastic differential equation dX t = a(X t )dW t + b(X t )dt, where W is a one-dimensional Brownian motion. We formulate the notion of solution and prove strong existence and pathwise uniqueness results when a is in C 1/2 and b is only a generalized function, for example,the distributional derivative of a Hölder function or of a function of bounded variation. When b = aa′, that is, when the generator of the SDE is the divergence form operator ℒ = , a result on non-existence of a strong solution and non-pathwise uniqueness is given as well as a result which characterizes when a solution is a semimartingale or not. We also consider extensions of the notion of Stratonovich integral.

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Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, Storrs, CT 06269, USA. e-mail: bass@math.uconn.edu., , , , , , US

    Richard F. Bass

  2. Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195-4350, USA. e-mail: zchen@math.washington.edu., , , , , , US

    Zhen-Qing Chens

Authors
  1. Richard F. Bass
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  2. Zhen-Qing Chens
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Additional information

Received: 23 February 2000 / Revised version: 22 January 2001 / Published online: 23 August 2001

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Bass, R., Chens, ZQ. Stochastic differential equations for Dirichlet processes. Probab Theory Relat Fields 121, 422–446 (2001). https://doi.org/10.1007/s004400100151

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  • Issue Date: November 2001

  • DOI: https://doi.org/10.1007/s004400100151

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Keywords

  • Differential Equation
  • Stochastic Differential Equation
  • Dirichlet Process
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