For multiparticle finite-state action evolutions, we prove that the observation σ-field admits a resolution involving a third noise which is generated by a random variable with uniform law. The Rees decomposition from semigroup theory and the theory of infinite convolutions are utilized in our proofs.
[1] J. Brossard and C. Leuridan. Chaˆınes de Markov constructives index´ees par Z. Ann.
Probab., 35(2):715–731, 2007.
[2] L. Chaumont and M. Yor. Exercises in probability. Cambridge Series in Statistical and
Probabilistic Mathematics. Cambridge University Press, Cambridge, second edition,
2012. A guided tour from measure theory to random processes, via conditioning.
[3] B. S. Cirel0 son. An example of a stochastic differential equation that has no strong
solution. Teor. Verojatnost. i Primenen., 20(2):427–430, 1975.
[4] H. S. Collins. Convergence of convolution iterates of measures. Duke Math. J.,
29:259–264, 1962.
[5] T. Hirayama and K. Yano. Extremal solutions for stochastic equations indexed by
negative integers and taking values in compact groups. Stochastic Process. Appl.,
120(8):1404–1423, 2010.
[6] G. H¨ogn¨as and A. Mukherjea. Probability measures on semigroups. Probability and
its Applications (New York). Springer, New York, second edition, 2011. Convolution
products, random walks, and random matrices.
[7] Y. Ito, T. Sera, and K. Yano. Examples of third noise problems for action evolutions
with infinite past. RIMS K¯
oky¯
uroku 2176, Proceedings of Research on the Theory of
Random Dynamical Systems and Fractal Geometry in 2019, pages 20–27, 2021.
[8] M. Rosenblatt. Limits of convolution sequences of measures on a compact topological
semigroup. J. Math. Mech., 9:293–305, 1960.
ˇ Schwarz. Convolution semigroup of measures on compact noncommutative semi[9] S.
groups. Czechoslovak Math. J., 14(89):95–115, 1964.
[10] A. N. Trahtman. The road coloring problem. Israel J. Math., 172:51–60, 2009.
[11] R. van Handel. On the exchange of intersection and supremum of σ-fields in filtering
theory. Israel J. Math., 192(2):763–784, 2012.
[12] K. Yano. Random walk in a finite directed graph subject to a road coloring. J.
Theoret. Probab., 26(1):259–283, 2013.
[13] K. Yano. Infinite convolutions of probability measures on polish semigroups. Probab.
Surv., 19:129–159, 2022.
[14] K. Yano and M. Yor. Around Tsirelson’s equation, or: The evolution process may
not explain everything. Probab. Surv., 12:1–12, 2015.
[15] M. Yor. Tsirel0 son’s equation in discrete time.
91(2):135–152, 1992.
30
Probab. Theory Related Fields,
...
全国の大学の
卒論・修論・学位論文
を
一発検索！
論文の公開元へ