%0 Journal Article %1 dawson-kurtz-82 %A Dawson, Donald %A Kurtz, Thomas %D 1982 %J Advances in Filtering and Optimal Stochastic Control %K duality measure_valued_process %P 91--105 %T Applications of duality to measure-valued diffusion processes %U http://dx.doi.org/10.1007/BFb0004528 %X Examples of measure-valued diffusion processes arise in nonlinear filtering theory as solutions of stochastic partial differential equations which describe the evolution of the normalized and unnormalized conditional distributions. In other applications such as population genetics examples of measure-valued diffu- sions have arisen which cannot be obtained as strong solutions of stochastic par- tial differential equations. In these examples the probability law of the measure- valued process is characterized as the unique solution of a martingale problem. In this approach to measure-valued diffusion processes a key role is played by the notion of a dual process which was originally introduced in the study of infi- nite particle systems. The purpose of this paper is to describe the martingale problem formulation of measure-valued diffusion processes with special emphasis on the role of duality and to present a number of examples.

@article{dawson-kurtz-82, abstract = { Examples of measure-valued diffusion processes arise in nonlinear filtering theory as solutions of stochastic partial differential equations which describe the evolution of the normalized and unnormalized conditional distributions. In other applications such as population genetics examples of measure-valued diffu- sions have arisen which cannot be obtained as strong solutions of stochastic par- tial differential equations. In these examples the probability law of the measure- valued process is characterized as the unique solution of a martingale problem. In this approach to measure-valued diffusion processes a key role is played by the notion of a dual process which was originally introduced in the study of infi- nite particle systems. The purpose of this paper is to describe the martingale problem formulation of measure-valued diffusion processes with special emphasis on the role of duality and to present a number of examples. }, added-at = {2009-04-07T03:22:43.000+0200}, author = {Dawson, Donald and Kurtz, Thomas}, biburl = {https://www.bibsonomy.org/bibtex/2e300aef96968e57c7eac1e3b4aa1b807/peter.ralph}, description = {Applications of duality to measure-valued diffusion processes}, interhash = {8e86d2b489894c46056f27d07f3b56b1}, intrahash = {e300aef96968e57c7eac1e3b4aa1b807}, journal = {Advances in Filtering and Optimal Stochastic Control}, keywords = {duality measure_valued_process}, pages = {91--105}, timestamp = {2009-04-07T03:22:43.000+0200}, title = {Applications of duality to measure-valued diffusion processes}, url = {http://dx.doi.org/10.1007/BFb0004528}, year = 1982 }