Guardado en:
| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2501.02655 |
| Etiquetas: |
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- In the paper we suggest a new construction of stochastic flows of kernels in a locally compact separable metric space $M$. Starting from a consistent sequence of Feller transtition function $(\mathsf{P}^{(n)}: n\geq 1)$ on $M$ we prove existence of a stochastic flow of kernels $K=(K_{s,t}: -\infty<s\leq t<\infty)$ in $M,$ such that distributions of $n$-point motions of $K$ are determined by $\mathsf{P}^{(n)}.$ Presented construction allows to find a single idempotent measurable presentation $\mathfrak{p}$ of distributions of all kernels $K_{s,t}$ from the flow, and to construct a flow that is invariant under $\mathfrak{p}$ and is jointly measurable in all arguments.